@article{ASENS_2001_4_34_4_525_0, author = {Demailly, Jean-Pierre and Koll\'ar, J\'anos}, title = {Semi-continuity of complex singularity exponents and {K\"ahler-Einstein} metrics on {Fano} orbifolds}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {525--556}, publisher = {Elsevier}, volume = {Ser. 4, 34}, number = {4}, year = {2001}, doi = {10.1016/s0012-9593(01)01069-2}, zbl = {0994.32021}, language = {en}, url = {http://www.numdam.org/articles/10.1016/s0012-9593(01)01069-2/} }
TY - JOUR AU - Demailly, Jean-Pierre AU - Kollár, János TI - Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds JO - Annales scientifiques de l'École Normale Supérieure PY - 2001 SP - 525 EP - 556 VL - 34 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/s0012-9593(01)01069-2/ DO - 10.1016/s0012-9593(01)01069-2 LA - en ID - ASENS_2001_4_34_4_525_0 ER -
%0 Journal Article %A Demailly, Jean-Pierre %A Kollár, János %T Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds %J Annales scientifiques de l'École Normale Supérieure %D 2001 %P 525-556 %V 34 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/s0012-9593(01)01069-2/ %R 10.1016/s0012-9593(01)01069-2 %G en %F ASENS_2001_4_34_4_525_0
Demailly, Jean-Pierre; Kollár, János. Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 34 (2001) no. 4, pp. 525-556. doi : 10.1016/s0012-9593(01)01069-2. http://www.numdam.org/articles/10.1016/s0012-9593(01)01069-2/
[1] Effective freeness and point separation for adjoint bundles, Invent. Math. 122 (1995) 291-308. | MR | Zbl
, ,[2] Carleman estimates for the Laplace-Beltrami equation in complex manifolds, Publ. Math. I.H.E.S. 25 (1965) 81-130. | Numdam | MR | Zbl
, ,[3] Singularities of Differentiable Maps, Progress in Math., Birkhäuser, 1985. | MR
, , ,[4] Équations du type Monge-Ampère sur les variétés kählériennes compactes, C. R. Acad. Sci. Paris Ser. A 283 (1976) 119-121, Bull. Sci. Math. 102 (1978) 63-95. | Zbl
,[5] Développements asymptotiques des fonctions obtenues par intégration sur les fibres, Invent. Math. 68 (1982) 129-174. | MR | Zbl
,[6] Algebraic values of meromorphic maps, Invent. Math. 10 (1970) 267-287, Addendum, Invent. Math. 11 (1970) 163-166. | MR | Zbl
,[7] New Sasakian-Einstein 5-manifolds as links of isolated hypersurface singularities, Manuscript, February 2000.
, ,[8] Nombres de Lelong généralisés, théorèmes d'intégralité et d'analyticité, Acta Math. 159 (1987) 153-169. | MR | Zbl
,[9] Transcendental proof of a generalized Kawamata-Viehweg vanishing theorem, C. R. Acad. Sci. Paris Sér. I Math. 309 (1989) 123-126, in: , (Eds.), Proceedings of the Conference “Geometrical and Algebraical Aspects in Several Complex Variables” held at Cetraro (Italy), 1989, pp. 81-94. | Zbl
,[10] Singular hermitian metrics on positive line bundles, in: , , , (Eds.), Proc. Conf. Complex algebraic varieties (Bayreuth, April 2-6, 1990), Lecture Notes in Math., 1507, Springer-Verlag, Berlin, 1992. | Zbl
,[11] Regularization of closed positive currents and intersection theory, J. Alg. Geom. 1 (1992) 361-409. | MR | Zbl
,[12] Monge-Ampère operators, Lelong numbers and intersection theory, in: , (Eds.), Complex Analysis and Geometry, Univ. Series in Math., Plenum Press, New York, 1993. | Zbl
,[13] A numerical criterion for very ample line bundles, J. Differential Geom. 37 (1993) 323-374. | MR | Zbl
,[14] L2 vanishing theorems for positive line bundles and adjunction theory, Lecture Notes of the CIME Session, Transcendental Methods in Algebraic Geometry, Cetraro, Italy, July 1994, 96 p, Duke e-prints alg-geom/9410022. | Zbl
,[15] Weighted projective varieties, in: Group Actions and Vector Fields, Proc. Polish-North Am. Semin., Vancouver 1981, Lect. Notes in Math., 956, Springer-Verlag, 1982, pp. 34-71. | Zbl
,[16] Working with weighted complete intersections, Preprint MPI/89-35, Max-Planck Institut für Mathematik, Bonn, 1989, Revised version: Iano-Fletcher A.R., in: Corti A., Reid M. (Eds.), Explicit Birational Geometry of 3-folds, Cambridge Univ. Press, 2000, pp. 101-173. | Zbl
,[17] On the fundamental group of certain open normal surfaces, Saitama Math. J. 11 (1993) 15-20. | MR | Zbl
, , ,[18] An obstruction to the existence of Einstein-Kähler metrics, Invent. Math. 73 (1983) 437-443. | Zbl
,[19] Resolution of singularities of an algebraic variety over a field of characteristic zero, I, II, Ann. Math. 79 (1964) 109-326. | MR | Zbl
,[20] An Introduction to Complex Analysis in Several Variables, North-Holland Math. Libr., 7, North-Holland, Amsterdam, 1973. | MR | Zbl
,[21] Kähler-Einstein metrics on log del Pezzo surfaces in weighted projective 3-spaces, Ann. Inst. Fourier 51 (2001) 69-79. | Numdam | Zbl
, ,[22] Introduction to the minimal model problem, Adv. Stud. Pure Math. 10 (1987) 283-360. | MR | Zbl
, , ,[23] Flips and Abundance for Algebraic Threefolds, Astérisque, 211, 1992. | Zbl
, (with 14 coauthors) ,[24] Shafarevich Maps and Automorphic Forms, Princeton Univ. Press, 1995. | MR | Zbl
,[25] Singularities of pairs, Algebraic Geometry, Santa Cruz, 1995, in: Proceedings of Symposia in Pure Math. Vol. 62, AMS, 1997, pp. 221-287. | MR | Zbl
,[26] Intégration sur un ensemble analytique complexe, Bull. Soc. Math. France 85 (1957) 239-262. | Numdam | MR | Zbl
,[27] Plurisubharmonic Functions and Positive Differential Forms, Gordon and Breach, New York, and Dunod, Paris, 1969. | Zbl
,[28] Sur les transformations analytiques des variétés kählériennes, C. R. Acad. Sci. Paris 244 (1957) 3011-3014. | MR | Zbl
,[29] An upper semicontinuity theorem for some leading poles of |f|2s, in: Complex Analytic Singularities, Adv. Stud. Pure Math., 8, North-Holland, Amsterdam, 1987, pp. 241-272. | MR | Zbl
,[30] Poles of |f(z,w)|2s and roots of the B-function, Ark. för Math. 27 (1989) 283-304. | MR | Zbl
,[31] Un théorème de prolongement L2 de sections holomorphes d'un fibré vectoriel, Math. Z. 212 (1993) 107-122. | MR | Zbl
,[32] Sur la structure du groupe d'homéomorphismes analytiques d'une certaine variété kählérienne, Nagoya Math. J. 11 (1957) 145-150. | MR | Zbl
,[33] Multiplier ideal sheaves and existence of Kähler-Einstein metrics of positive scalar curvature, Proc. Nat. Acad. Sci. USA 86 (1989) 7299-7300. | Zbl
,[34] Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature, Annals of Math. 132 (1990) 549-596. | Zbl
,[35] On the extension of L2 holomorphic functions, Math. Z. 195 (1987) 197-204. | MR | Zbl
, ,[36] On the extension of L2 holomorphic functions, II, Publ. RIMS, Kyoto Univ. 24 (1988) 265-275. | MR | Zbl
,[37] Algebraic estimates, stability of local zeta functions, and uniform estimates for distribution functions, preprint, January 1999, to appear in Ann. of Math. | MR | Zbl
, ,[38] On a conjecture of Demailly and Kollár, preprint, April 2000. | MR
, ,[39] 3-fold log flips, Izv. Russ. Acad. Nauk Ser. Mat. 56 (1992) 105-203. | MR
,[40] Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Invent. Math. 27 (1974) 53-156. | MR | Zbl
,[41] Lectures on Hermitian-Einstein metrics for stable bundles and Kähler-Einstein metrics, DMV Seminar (Band 8), Birkhäuser-Verlag, Basel, 1987. | Zbl
,[42] The existence of Kähler-Einstein metrics on manifolds with positive anticanonical line bundle and a suitable finite symmetry group, Ann. of Math. 127 (1988) 585-627. | Zbl
,[43] An effective Matsusaka big theorem, Ann. Inst. Fourier. 43 (1993) 1387-1405. | Numdam | MR | Zbl
,[44] Sous-ensembles analytiques d'ordre fini ou infini dans Cn, Bull. Soc. Math. France 100 (1972) 353-408. | Numdam | MR | Zbl
,[45] Estimations L2 pour l’opérateur et applications arithmétiques, in: Séminaire P. Lelong (Analyse), année 1975/76, Lecture Notes in Math., 538, Springer-Verlag, Berlin, 1977, pp. 314-323. | Zbl
,[46] On Kähler-Einstein metrics on certain Kähler manifolds with c1(M)>0, Invent. Math. 89 (1987) 225-246. | Zbl
,[47] Complex exponents of a singularity do not change along the stratum μ=constant, Functional Anal. Appl. 16 (1982) 1-9. | Zbl
,[48] Semi-continuity of the complex singularity index, Functional Anal. Appl. 17 (1983) 307-308. | Zbl
,[49] Asymptotic Hodge structure …, Math. USSR Izv. 18 (1992) 469-512. | Zbl
,[50] On the Ricci curvature of a complex Kähler manifold and the complex Monge-Ampère equation I, Comm. Pure and Appl. Math. 31 (1978) 339-411. | Zbl
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