Courants kählériens et surfaces compactes

Lamari, Ahcène

doi:10.5802/aif.1673

Lamari, Ahcène

Annales de l'Institut Fourier, Tome 49 (1999) no. 1, pp. 263-285.

Résumé
Abstract

Le théorème de régularisation de Demailly ramène l’existence d’une métrique kählérienne sur une surface compacte à celle d’un (1-1)-courant strictement positif $d$ -fermé (“courant kählérien”). Après avoir démontré un critère d’existence d’un tel courant, nous utilisons la symétrie de Hodge pour donner une démonstration unifiée du caractère kählérien des surfaces compactes à premier nombre de Betti pair.

A compact complex surface is shown to be Kähler if and only if it carries a strictly positive $d$ -closed current (in other words, a Kähler current), thanks to Demailly’s regularization theorem. We prove a Harvey-Lawson type characterization of compact manifolds carrying such a current. Using Hodge symmetry, we then give a unified proof of kählerianity for surfaces with even first Betti number.

MR Zbl | 6 citations dans Numdam

DOI : 10.5802/aif.1673

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Lamari, Ahcène. Courants kählériens et surfaces compactes. Annales de l'Institut Fourier, Tome 49 (1999) no. 1, pp. 263-285. doi : 10.5802/aif.1673. https://www.numdam.org/articles/10.5802/aif.1673/

Bibliographie
Cité par

[BPV84] W. Barth, C. Peters et A. Van De Ven, Compact complex surfaces, Springer, Berlin, 1984. | MR | Zbl

[Be85] A. Beauville, Toutes les surfaces K3 sont kählériennes, Astérisque 126, Paris (1985). | Numdam | Zbl

[CK52] W.-L. Chow et K. Kodaira, On analytic surfaces with two independent meromorphic functions, Proc. Nat. Acad. Sci. U.S.A., 38 (1952), 319-325. | MR | Zbl

[De92] J.-P. Demailly, Regularization of closed positive currents and intersection theory, J. Alg. Geom., 1 (1992), 361-409. | MR | Zbl

[De93] J.-P. Demailly, Monge-Ampère operators, Lelong numbers and intersection theory, in Complex Analysis and Geometry, Univ. Series in Math., edited by V. Ancona and A. Silva, Plenum Press, New-York, 1993. | MR | Zbl

[F83] A. Fujiki, On compact complex manifolds in C without holomorphic 2-forms Publ. Res. Inst. Math. Sci. Kyoto, 19 (1983), 193-202. | MR | Zbl

[Gau77] P. Gauduchon, Le théorème de l'excentricité nulle, C. R. Acad. Sci. Paris, série A, 285 (1977), 387-390. | MR | Zbl

[Gau85] P. Gauduchon, Les métriques standard sur une surface à b1 pair, Astérisque 126, Paris (1985).

[H74] R. Harvey, Removable singularities for positive currents, Amer. J. Math., 96 (1974), 67-78. | MR | Zbl

[H77] R. Harvey, Holomorphic chains and their boundaries Proc. Symp. Pure Math., 30, Part I, AMS, Providence, R.I. (1977), 309-382. | MR | Zbl

[Hi75] H. Hironaka, Flattening theorem in complex analytic geometry, Amer. J. Math., 97 (1975), 503-547. | MR | Zbl

[HL83] R. Harvey et H.B. Jr Lawson, An intrinsic characterization of Kähler manifolds, Invent. Math., 74 (1983), 261-295. | Zbl

[JS93] S. Ji et B. Shiffman, Properties of compact complex manifolds carrying closed positive currents, J. Geom. Anal., 3 (1993), 37-62. | MR | Zbl

[Ji93] S. Ji, Currents, metrics and Moishezon manifolds, Pacific Journal of Math., 158 (1993), 335-351. | MR | Zbl

[K64] K. Kodaira, On the structure of compact complex analytic surfaces (I), Amer. J. Math., 86 (1964), 751-798. | MR | Zbl

[KM71] K. Kodaira et J. Morrow, Complex manifolds, New York: Holt, Rinehart and Winston, 1971. | MR | Zbl

[Le68] P. Lelong, Fonctions plurisousharmoniques et formes différentielles positives, Dunod, Paris, 1968. | MR | Zbl

[M83] M.-L. Michelsohn, On the existence of special metrics in complex geometry, Acta Math., 143 (1983), 261-295. | Zbl

[Miy74a] Y. Miyaoka, Extension theorems for Kähler metrics, Proc. Japan Acad., 50 (1974), 407-410. | MR | Zbl

[Miy74b] Y. Miyaoka, Kähler metrics on elliptic surfaces, Proc. Japan Acad., 50 (1974), 533-536. | MR | Zbl

[Sh] B. Shiffman, Extension of positive line bundles and meromorphic maps, Invent. Math., 15 (1972), 332-347. | MR | Zbl

[Siu74] Y.-T. Siu, Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Invent. Math., 27 (1974), 53-156. | MR | Zbl

[Siu83] Y.-T. Siu, Every K3 surface is Kähler, Invent. Math., 73 (1983), 130-150. | MR | Zbl

[Su76] D. Sullivan, Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math., 36 (1976), 225-255. | MR | Zbl

[V] J. Varouchas, Propriétés cohomologiques d'une classe de variétés analytiques complexes compactes, Sem. d'Analyse Lelong-Dolbeault-Skoda 1983-1984, Lecture Notes in Math., Vol. 1198, Springer, Berlin, 1985, 245-259. | Zbl

Fino, Anna Canonical metrics in complex geometry, Bollettino dell'Unione Matematica Italiana, Volume 18 (2025) no. 1, p. 185 | DOI:10.1007/s40574-024-00421-y
Li, Yinji; Wang, Zhiwei; Zhou, Xiangyu A Note on Demailly’s Transcendental Morse Inequalities Conjecture, Frontiers of Mathematics (2025) | DOI:10.1007/s11464-024-0145-y
Popovici, Dan; Stelzig, Jonas; Ugarte, Luis Higher-page Hodge theory of compact complex manifolds, Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V, Volume 25 (2024) no. 3, pp. 1431-1464 | DOI:10.2422/2036-2145.202111_014 | Zbl:7944256
Marouani, Samir SKT hyperbolic and Gauduchon hyperbolic compact complex manifolds, Bulletin de la Société Mathématique de France, Volume 152 (2024) no. 3, pp. 519-545 | DOI:10.24033/bsmf.2894 | Zbl:1551.32035
Rao, Sheng; Zou, Yongpan $\partial \overset{―}{\partial}$ -Lemma and Double Complex, Communications in Mathematics and Statistics (2024) | DOI:10.1007/s40304-024-00400-x
Sillari, Lorenzo; Tomassini, Adriano On the spaces of $(d + d^{c})$ -harmonic forms and $(d + d^{Λ})$ -harmonic forms on almost Hermitian manifolds and complex surfaces, Revista Matemática Iberoamericana, Volume 40 (2024) no. 6, pp. 2371-2398 | DOI:10.4171/rmi/1492 | Zbl:7958550
Li, Yinji; Wang, Zhiwei; Zhou, Xiangyu Degenerate complex Monge-Ampère type equations on compact Hermitian manifolds and applications, Transactions of the American Mathematical Society, Volume 377 (2024) no. 8, pp. 5947-5992 | DOI:10.1090/tran/9199 | Zbl:1544.32069
Sompurkar, Rajas Sandeep Existence of higher extremal Kähler metrics on a minimal ruled surface, Bulletin des Sciences Mathématiques, Volume 189 (2023), p. 39 (Id/No 103345) | DOI:10.1016/j.bulsci.2023.103345 | Zbl:1533.53058
Entov, Michael; Verbitsky, Misha Rigidity of Lagrangian embeddings into symplectic tori and K3 surfaces, International Mathematics Research Notices, Volume 2023 (2023) no. 10, p. 8964 | DOI:10.1093/imrn/rnac107
Entov, Michael; Verbitsky, Misha Kähler-type embeddings of balls into symplectic manifolds, Journal of the Association for Mathematical Research, Volume 1 (2023) no. 1, pp. 16-119 | Zbl:1551.53096
Apostolov, Vestislav; Dloussky, Georges Twisted differentials and Lee classes of locally conformally symplectic complex surfaces, Mathematische Zeitschrift, Volume 303 (2023) no. 3, p. 33 (Id/No 76) | DOI:10.1007/s00209-023-03242-5 | Zbl:1510.32036
Marouani, Samir; Popovici, Dan Some properties of balanced hyperbolic compact complex manifolds, International Journal of Mathematics, Volume 33 (2022) no. 3, p. 39 (Id/No 2250019) | DOI:10.1142/s0129167x22500197 | Zbl:1487.32147
Holt, Tom Bott-Chern and $\bar{\partial}$ harmonic forms on almost Hermitian 4-manifolds, Mathematische Zeitschrift, Volume 302 (2022) no. 1, pp. 47-72 | DOI:10.1007/s00209-022-03048-x | Zbl:1496.32035
Tan, Qiang; Wang, Hongyu; Zhou, Jiuru; Zhu, Peng On tamed almost complex four-manifolds, Peking Mathematical Journal, Volume 5 (2022) no. 1, pp. 37-152 | DOI:10.1007/s42543-021-00045-7 | Zbl:1519.53069
Dinew, Sławomir; Popovici, Dan A generalised volume invariant for Aeppli cohomology classes of Hermitian-symplectic metrics, Advances in Mathematics, Volume 393 (2021), p. 46 (Id/No 108056) | DOI:10.1016/j.aim.2021.108056 | Zbl:1521.32018
Albanese, Michael The Yamabe invariants of Inoue surfaces, Kodaira surfaces, and their blowups, Annals of Global Analysis and Geometry, Volume 59 (2021) no. 2, pp. 179-195 | DOI:10.1007/s10455-020-09744-3 | Zbl:1459.53067
Tosatti, Valentino Ricci-flat metrics and dynamics on $K 3$ surfaces, Bollettino dell'Unione Matematica Italiana, Volume 14 (2021) no. 1, pp. 191-209 | DOI:10.1007/s40574-020-00269-y | Zbl:1464.14042
Rao, Sheng; Tsai, I-Hsun Deformation limit and bimeromorphic embedding of Moishezon manifolds, Communications in Contemporary Mathematics, Volume 23 (2021) no. 8, p. 50 (Id/No 2050087) | DOI:10.1142/s021919972050087x | Zbl:1484.32020
Meng, Lingxu The heredity and bimeromorphic invariance of the $\partial \bar{\partial}$ -lemma property, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 359 (2021) no. 6, pp. 645-650 | DOI:10.5802/crmath.203 | Zbl:1477.32050
Latorre, Adela; Ugarte, Luis On the stability of compact pseudo-Kähler and neutral Calabi-Yau manifolds, Journal de Mathématiques Pures et Appliquées. Neuvième Série, Volume 145 (2021), pp. 240-262 | DOI:10.1016/j.matpur.2020.09.001 | Zbl:1457.53050
Verbitsky, Mikhail S.; Vuletescu, Victor; Ornea, Liviu Classification of non-Kähler surfaces and locally conformally Kähler geometry, Russian Mathematical Surveys, Volume 76 (2021) no. 2, pp. 261-289 | DOI:10.1070/rm9858 | Zbl:1471.32023
Verbitsky, Mikhail Sergeevich; Vuletescu, Victor; Ornea, Liviu Классификация некэлеровых поверхностей и локально конформно кэлерова геометрия, Успехи математических наук, Volume 76 (2021) no. 2(458), p. 71 | DOI:10.4213/rm9858
Angella, Daniele; Sferruzza, Tommaso Geometric formalities Along the Chern-Ricci flow, Complex Analysis and Operator Theory, Volume 14 (2020) no. 1, p. 29 (Id/No 27) | DOI:10.1007/s11785-019-00971-6 | Zbl:1436.53048
Angella, Daniele; Suwa, Tatsuo; Tardini, Nicoletta; Tomassini, Adriano Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms, Complex Manifolds, Volume 7 (2020), pp. 194-214 | DOI:10.1515/coma-2020-0103 | Zbl:1462.32021
Yang, Xiaokui RC-positive metrics on rationally connected manifolds, Forum of Mathematics, Sigma, Volume 8 (2020), p. 19 (Id/No e53) | DOI:10.1017/fms.2020.32 | Zbl:1454.53061
Streets, Jeffrey Pluriclosed flow and the geometrization of complex surfaces, Geometric analysis. In honor of Gang Tian's 60th birthday, Cham: Birkhäuser, 2020, pp. 471-510 | DOI:10.1007/978-3-030-34953-0_19 | Zbl:1444.32018
Angella, Daniele; Cirici, Joana; Demailly, Jean-Pierre; Wilson, Scott Mini-workshop: Almost complex geometry. Abstracts from the mini-workshop held October 4–10, 2020 (online meeting), Oberwolfach Rep. 17, No. 4, 1657-1691, 2020 | DOI:10.4171/owr/2020/33 | Zbl:1473.00037
Wang, Zhi Wei On Grauert-Riemenschneider type criteria, Acta Mathematica Sinica. English Series, Volume 35 (2019) no. 5, pp. 609-618 | DOI:10.1007/s10114-019-8123-0 | Zbl:1417.53079
Angella, Daniele; Tomassini, Adriano; Verbitsky, Misha On non-Kähler degrees of complex manifolds, Advances in Geometry, Volume 19 (2019) no. 1, pp. 65-69 | DOI:10.1515/advgeom-2018-0026 | Zbl:1416.32011
Yang, Xiaokui A partial converse to the Andreotti-Grauert theorem, Compositio Mathematica, Volume 155 (2019) no. 1, pp. 89-99 | DOI:10.1112/s0010437x18007509 | Zbl:1430.14044
Yang, Xiaokui Scalar curvature on compact complex manifolds, Transactions of the American Mathematical Society, Volume 371 (2019) no. 3, pp. 2073-2087 | DOI:10.1090/tran/7409 | Zbl:1430.53079
Angella, Daniele; Tomassini, Adriano Hermitian ranks of compact complex manifolds, Proceedings of the American Mathematical Society, Volume 146 (2018) no. 5, pp. 2195-2205 | DOI:10.1090/proc/13938 | Zbl:1396.32012
Popovici, Dan; Ugarte, Luis Compact complex manifolds with small Gauduchon cone, Proceedings of the London Mathematical Society. Third Series, Volume 116 (2018) no. 5, pp. 1161-1186 | DOI:10.1112/plms.12110 | Zbl:1394.32013
Rao, Sheng; Zhao, Quanting Several special complex structures and their deformation properties, The Journal of Geometric Analysis, Volume 28 (2018) no. 4, pp. 2984-3047 | DOI:10.1007/s12220-017-9944-7 | Zbl:1420.32006
Grantcharov, Gueo; Lejmi, Mehdi; Verbitsky, Misha Existence of HKT metrics on hypercomplex manifolds of real dimension 8, Advances in Mathematics, Volume 320 (2017), pp. 1135-1157 | DOI:10.1016/j.aim.2017.09.020 | Zbl:1390.53046
Alessandrini, Lucia Product of generalized $p$ -Kähler manifolds, Annali di Matematica Pura ed Applicata. Serie Quarta, Volume 196 (2017) no. 5, pp. 1835-1853 | DOI:10.1007/s10231-017-0640-9 | Zbl:1381.53134
Lejmi, Mehdi; Weber, Patrick Cohomologies on Hypercomplex Manifolds, Complex and Symplectic Geometry, Volume 21 (2017), p. 107 | DOI:10.1007/978-3-319-62914-8_9
Xiao, Jian Characterizing volume via cone duality, Mathematische Annalen, Volume 369 (2017) no. 3-4, pp. 1527-1555 | DOI:10.1007/s00208-016-1501-3 | Zbl:1379.32015
LEJMI, MEHDI; WEBER, PATRICK QUATERNIONIC BOTT–CHERN COHOMOLOGY AND EXISTENCE OF HKT METRICS, The Quarterly Journal of Mathematics (2017) | DOI:10.1093/qmath/haw060
Nguyen, Ngoc Cuong The complex Monge-Ampère type equation on compact Hermitian manifolds and applications, Advances in Mathematics, Volume 286 (2016), pp. 240-285 | DOI:10.1016/j.aim.2015.09.009 | Zbl:1337.53088
Wang, Zhiwei On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold, Annales Polonici Mathematici, Volume 117 (2016) no. 1, pp. 41-58 | DOI:10.4064/ap3780-11-2015 | Zbl:1357.53084
Angella, Daniele; Dloussky, Georges; Tomassini, Adriano On Bott-Chern cohomology of compact complex surfaces, Annali di Matematica Pura ed Applicata. Serie Quarta, Volume 195 (2016) no. 1, pp. 199-217 | DOI:10.1007/s10231-014-0458-7 | Zbl:1343.32012
Xiao, Jian A remark on the convergence of the inverse $σ_{k}$ -flow, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 354 (2016) no. 4, pp. 395-399 | DOI:10.1016/j.crma.2016.01.016 | Zbl:1381.53126
Apostolov, Vestislav; Dloussky, Georges Locally Conformally Symplectic Structures on Compact Non-Kähler Complex Surfaces, International Mathematics Research Notices, Volume 2016 (2016) no. 9, p. 2717 | DOI:10.1093/imrn/rnv211
Popovici, Dan Sufficient bigness criterion for differences of two nef classes, Mathematische Annalen, Volume 364 (2016) no. 1-2, pp. 649-655 | DOI:10.1007/s00208-015-1230-z | Zbl:1341.32015
Panov, Taras; Ustinovskiy, Yury; Verbitsky, Misha Complex geometry of moment-angle manifolds, Mathematische Zeitschrift, Volume 284 (2016) no. 1-2, pp. 309-333 | DOI:10.1007/s00209-016-1658-1 | Zbl:1352.32008
Chiose, Ionuţ The Kähler rank of compact complex manifolds, The Journal of Geometric Analysis, Volume 26 (2016) no. 1, pp. 603-615 | DOI:10.1007/s12220-015-9564-z | Zbl:1348.32007
Alessandrini, Lucia Holomorphic submersions onto Kähler or balanced manifolds, Tohoku Mathematical Journal, Volume 68 (2016) no. 4 | DOI:10.2748/tmj/1486177218
Xiao, Jian Weak transcendental holomorphic Morse inequalities on compact Kähler manifolds, Annales de l'Institut Fourier, Volume 65 (2015) no. 3, pp. 1367-1379 | DOI:10.5802/aif.2959 | Zbl:1333.32025
Moroianu, Andrei Compact lcK manifolds with parallel vector fields, Complex Manifolds, Volume 2 (2015), pp. 26-33 | DOI:10.1515/coma-2015-0004 | Zbl:1320.32024
Tan, Qiang; Wang, Hongyu; Zhang, Ying; Zhu, Peng On cohomology of almost complex 4-manifolds, The Journal of Geometric Analysis, Volume 25 (2015) no. 3, pp. 1431-1443 | DOI:10.1007/s12220-014-9477-2 | Zbl:1323.53081
Xiao, Jian On strongly Gauduchon metrics of compact complex manifolds, The Journal of Geometric Analysis, Volume 25 (2015) no. 3, pp. 2011-2027 | DOI:10.1007/s12220-014-9502-5 | Zbl:1327.32032
Pontecorvo, Massimiliano On a question of Vaisman concerning complex surfaces, Annali di Matematica Pura ed Applicata. Serie Quarta, Volume 193 (2014) no. 5, pp. 1283-1293 | DOI:10.1007/s10231-013-0328-8 | Zbl:1304.53076
Otoba, Nobuhiko Constant scalar curvature metrics on Hirzebruch surfaces, Annals of Global Analysis and Geometry, Volume 46 (2014) no. 3, pp. 197-223 | DOI:10.1007/s10455-014-9419-z | Zbl:1302.53039
Angella, Daniele Preliminaries on (Almost-)Complex Manifolds, Cohomological Aspects in Complex Non-Kähler Geometry, Volume 2095 (2014), p. 1 | DOI:10.1007/978-3-319-02441-7_1
Angella, Daniele Cohomology of Almost-Complex Manifolds, Cohomological Aspects in Complex Non-Kähler Geometry, Volume 2095 (2014), p. 151 | DOI:10.1007/978-3-319-02441-7_4
Angella, Daniele Cohomology of Complex Manifolds, Cohomological Aspects in Complex Non-Kähler Geometry, Volume 2095 (2014), p. 65 | DOI:10.1007/978-3-319-02441-7_2
Chiose, Ionuţ Obstructions to the existence of Kähler structures on compact complex manifolds, Proceedings of the American Mathematical Society, Volume 142 (2014) no. 10, pp. 3561-3568 | DOI:10.1090/s0002-9939-2014-12128-9 | Zbl:1310.32023
Ugarte, Luis Special Hermitian metrics, complex nilmanifolds and holomorphic deformations, Revista de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza. Serie 2, Volume 69 (2014), pp. 7-35 | Zbl:7989191
Popovici, Dan Deformation limits of projective manifolds: Hodge numbers and strongly Gauduchon metrics, Inventiones Mathematicae, Volume 194 (2013) no. 3, pp. 515-534 | DOI:10.1007/s00222-013-0449-0 | Zbl:1287.32008
Tosatti, Valentino; Weinkove, Ben Plurisubharmonic functions and nef classes on complex manifolds, Proceedings of the American Mathematical Society, Volume 140 (2012) no. 11, pp. 4003-4010 | DOI:10.1090/s0002-9939-2012-11206-7 | Zbl:1273.53063
Deschamps, Guillaume Compatible complex structures on twistor space, Annales de l'Institut Fourier, Volume 61 (2011) no. 6, pp. 2219-2248 | DOI:10.5802/aif.2671 | Zbl:1267.53051
Toma, Matei On the Kähler rank of compact complex surfaces, Bulletin de la Société Mathématique de France, Volume 136 (2008) no. 2, pp. 243-260 | DOI:10.24033/bsmf.2556 | Zbl:1165.32010
Apostolov, Vestislav; Gualtieri, Marco Generalized Kähler manifolds, commuting complex structures, and split tangent bundles, Communications in Mathematical Physics, Volume 271 (2007) no. 2, pp. 561-575 | DOI:10.1007/s00220-007-0196-4 | Zbl:1135.53018
Teleman, Andrei The pseudo-effective cone of a non-Kählerian surface and applications, Mathematische Annalen, Volume 335 (2006) no. 4, pp. 965-989 | DOI:10.1007/s00208-006-0782-3 | Zbl:1096.32011
Buchdahl, Nicholas Algebraic deformations of compact Kähler surfaces, Mathematische Zeitschrift, Volume 253 (2006) no. 3, pp. 453-459 | DOI:10.1007/s00209-005-0910-x | Zbl:1118.32016
Fujiki, A.; Pontecorvo, M. On Hermitian Geometry of Complex Surfaces, Complex, Contact and Symmetric Manifolds, Volume 234 (2005), p. 153 | DOI:10.1007/0-8176-4424-5_11
Boucksom, Sébastien Divisorial Zariski decompositions on compact complex manifolds, Annales Scientifiques de l'École Normale Supérieure. Quatrième Série, Volume 37 (2004) no. 1, pp. 45-76 | DOI:10.1016/j.ansens.2003.04.002 | Zbl:1054.32010
Parton, Maurizio Hopf surfaces: locally conformal Kähler metrics and foliations, Annali di Matematica Pura ed Applicata, Volume 182 (2003) no. 3, p. 287 | DOI:10.1007/s10231-002-0066-9
Buchdahl, Nicholas Compact Kähler surfaces with trivial canonical bundle, Annals of Global Analysis and Geometry, Volume 23 (2003) no. 2, pp. 189-204 | DOI:10.1023/a:1022557004624 | Zbl:1049.14030
Boucksom, Sébastien On the volume of a line bundle., International Journal of Mathematics, Volume 13 (2002) no. 10, pp. 1043-1063 | DOI:10.1142/s0129167x02001575 | Zbl:1101.14008

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