Kobayashi-Hitchin correspondence for tame harmonic bundles and an application

Takuro, Mochizuki

Astérisque, no. 309 (2006) , 125 p.

@book{AST_2006__309__R1_0,
     author = {Takuro, Mochizuki},
     title = {Kobayashi-Hitchin correspondence for tame harmonic bundles and an application},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {309},
     year = {2006},
     mrnumber = {2310103},
     zbl = {1119.14001},
     language = {en},
     url = {http://www.numdam.org/item/AST_2006__309__R1_0/}
}

TY  - BOOK
AU  - Takuro, Mochizuki
TI  - Kobayashi-Hitchin correspondence for tame harmonic bundles and an application
T3  - Astérisque
PY  - 2006
IS  - 309
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2006__309__R1_0/
LA  - en
ID  - AST_2006__309__R1_0
ER  -

%0 Book
%A Takuro, Mochizuki
%T Kobayashi-Hitchin correspondence for tame harmonic bundles and an application
%S Astérisque
%D 2006
%N 309
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2006__309__R1_0/
%G en
%F AST_2006__309__R1_0

Takuro, Mochizuki. Kobayashi-Hitchin correspondence for tame harmonic bundles and an application. Astérisque, no. 309 (2006), 125 p. http://numdam.org/item/AST_2006__309__R1_0/

Bibliographie
Cité par

[1] L. V. Ahlfors - An extension of Schwarz's lemma, Trans. Amer. Math. Soc. 43 (1938), p. 359-364. | MR | JFM

[2] A. Andreotti & E. Vesentini - Carlman estimates for the Laplace-Beltrami equation on complex manifolds, Inst. Hautes Études Sci. Publ. Math. 25 (1965), p. 81-130. | MR | EuDML | Numdam | DOI

[3] T. Aubin - Nonlinear analysis on manifolds. Monge-Ampère equations, Springer-Verlag, Berlin-New York, 1982. | MR | Zbl

[4] O. Biquard - Sur les fibrés paraboliques sur une surface complexe, J. London Math. Soc. 53 (1996), no. 2, p. 302-316. | MR | Zbl | DOI

[5] O. Biquard, Fibrés de Higgs et connexions intégrables : le cas logarithmique (diviseur lisse), Ann. Sci. École Norm. Sup. 30 (1997), p. 41-96. | MR | EuDML | Zbl | Numdam | DOI

[6] K. Corlette - Flat $G$ -bundles with canonical metrics, J. Differential Geom. 28 (1988), p. 361-382. | MR | Zbl | DOI

[7] K. Corlette, Nonabelian Hodge theory, in Differential geometry : geometry in mathematical physics and related topics (Los Angeles, CA, 1990) , Part 2, Proc. Sym-pos. Pure Math., vol. 54, Amer. Math. Soc, Providence, RI, 1993, p. 125-144. | MR

[8] M. Cornalba & P. Griffiths - Analytic cycles and vector bundles on non-compact algebraic varieties, Invent. Math. 28 (1975), p. 1-106. | MR | EuDML | Zbl | DOI

[9] P. Deligne - Équations différentielles à points singuliers réguliers, Lecture Notes in Math., vol. 163, Springer-Verlag, Berlin-New York, 1970. | MR | Zbl

[10] P. Deligne, Un théorème de finitude pour la monodromie, in Discrete Groups in Geometry and Analysis, Birkhäuser, 1987, p. 1-19. | MR | Zbl

[11] P. Deligne, J. S. Milne, A. Ogus & K. Shih - Hodge cycles, motives, and Shimura varieties, Lecture Notes in Math., vol. 900, Springer-Verlag, Berlin-New York, 1982. | MR | Zbl

[12] S. K. Donaldson - A new proof of a theorem of Narasimhan and Seshadri, J. Differential Geom. 18 (1983), p. 269-277. | MR | Zbl | DOI

[13] S. K. Donaldson, Anti self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc. 50 (1985), p. 1-26. | MR | Zbl | DOI

[14] S. K. Donaldson, Infinite determinants, stable bundles and curvature, Duke Math. J. 54 (1987), p. 231-247. | MR | Zbl | DOI

[15] S. K. Donaldson, Twisted harmonic maps and the self-duality equations, Proc. London Math. Soc. 55 (1987), p. 127-131. | MR | Zbl | DOI

[16] K. Fukaya The gauge theory and topology, Springer-Verlag, Tokyo, 1995, in Japanese.

[17] W. Fulton - Intersection theory, second ed., Springer-Verlag, Berlin, 1988. | MR

[18] D. Gilbarg & N. Trudinger - Elliptic partial differential equations of second order, second ed., Springer-Verlag, Berlin, 1983. | MR | Zbl | DOI

[19] A. Grothendieck - Techniques de construction et théorèmes d'existence en géométrie algébrique IV : Les schémas de Hilbert, in Séminaire Bourbaki, IHP, Paris, 1961, exposé 221. | EuDML | Numdam | Zbl

[20] R. Hartshorne - Algebraic geometry, Springer-Verlag, New York-Heidelberg, 1977. | MR | Zbl | DOI

[21] R. Hartshorne, Stable reflexive sheaves, Math. Ann. 254 (1980), p. 121-176. | MR | EuDML | Zbl | DOI

[23] G. Hochshild - The structure of Lie groups, Holden-Day, 1965. | MR

[24] L. Hörmander - An introduction to complex analysis in several variables, North-Holland Publishing Co., Amsterdam, 1990. | MR | Zbl

[25] D. Huybrechts & M. Lehn - Framed modules and their moduli, Internat. J. Math. 6 (1995), p. 297-324. | MR | Zbl | DOI

[26] S. Ito - Functional Analysis, Iwanami Shoten, Tokyo, 1983, in Japanese. | MR

[27] J. Iyer & C. Simpson - A relation between the parabolic Chern characters of the de Rham bundles, math. AG/0603677. | MR | Zbl

[28] J. Jost, J. Li & K. Zuo - Harmonic bundles on quasi-compact Kaehler manifolds, math.AG/0108166.

[29] J. Jost & K. Zuo - Harmonic maps of infinite energy and rigidity results for representations of fundamental groups of quasiprojective varieties, J. Differential Geom. 47 (1997), p. 469-503. | MR | Zbl | DOI

[30] S. Kobayashi - First Chern class and holomorphic tensor fields, Nagoya Math. J. 77 (1980), p. 5-11. | MR | Zbl | DOI

[31] S. Kobayashi, Curvature and stability of vector bundles, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), p. 158-162. | MR | Zbl | DOI

[32] S. Kobayashi, Differential geometry of complex vector bundles, Princeton University Press/Iwanami Shoten, Princeton, NJ/Tokyo, 1987. | MR | Zbl | DOI

[33] S. Langton - Valuative criteria for families of vector bundles on algebraic varieties, Ann. of Math. 101 (1975), p. 88-110. | MR | Zbl | DOI

[34] J. Li - Hitchin's self-duality equations on complete Riemannian manifolds, Math. Ann. 306 (1996), p. 419-428. | MR | EuDML | Zbl | DOI

[35] J. Li, Hermitian-Einstein metrics and Chern number inequalities on parabolic stable bundles over Kähler manifolds, Comm. Anal. Geom. 8 (2000), p. 445-475. | MR | Zbl | DOI

[36] J. Li & M. S. Narasimhan - Hermitian-Einstein metrics on parabolic stable bundles, Acta Math. Sin. (Engl. Ser.) 15 (1999), p. 93-114. | MR | Zbl | DOI

[37] M. Lübke - Stability of Einstein-Hermitian vector bundles, Manuscripta Math. 42 (1983), p. 245-257. | MR | EuDML | Zbl | DOI

[38] M. Lübke & A. Teleman - The universal Kobayashi-Hitchin correspondence on Hermitian manifolds, math.DG/0402341, to appear in Mem. Amer. Math. Soc. | Zbl | MR | DOI

[39] M. Maruyama & K. Yokogawa - Moduli of parabolic stable sheaves, Math. Ann. 293 (1992), p. 77-99. | MR | EuDML | Zbl | DOI

[40] V. Mehta & A. Ramanathan Restriction of stable sheaves and representations of the fundamental group, Invent. Math. 77 (1984), p. 163-172. | MR | EuDML | Zbl | DOI

[41] V. Mehta & A. Ramanathan, Semistable sheaves on projective varieties and their restriction to curves, Math. Ann. 258 (1982), p. 213-224. | MR | EuDML | Zbl | DOI

[42] V. Mehta & C. S. Seshadri - Moduli of vector bundles on curves with parabolic structures, Math. Ann. 248 (1980), p. 205-239. | MR | EuDML | Zbl | DOI

[43] T. Mochizuki - Asymptotic behaviour of tame nilpotent harmonic bundles with trivial parabolic structure, J. Differential Geom. 62 (2002), p. 351-559. | MR | Zbl | DOI

[44] T. Mochizuki, Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules, to appear in Mem. Amer. Math. Soc., the final version is available from http://www.math.kyoto-u.ac.jp/~takuro/twistor.pdf. | MR | Zbl

[45] T. Mochizuki, A characterization of semisimple local system by tame pure imaginary pluri-harmonic metric, math.DG/0402122, to appear as a part of [44].

[46] T. Mochizuki, Kobayahi-Hitchin correspondence for tame harmonic bundles and an application II, math.DG/0602266.

[47] M. S. Narasimhan & C. S. Seshadri Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math. 82 (1965), p. 540-567. | MR | Zbl | DOI

[48] R. Palais - Foundations of global non-linear analysis, Benjamin, 1968. | MR | Zbl

[49] J. Poritz - Parabolic vector bundles and Hermitian-Yang-Mills connections over a Riemann surface, Internat. J. Math. 4 (1993), p. 467-501. | MR | Zbl | DOI

[50] C. Sabbah - Polarizable twistor $D$ -modules, Astérisque, vol. 300, Soc. Math. France, Paris, 2005. | MR | Zbl | Numdam

[51] C. Simpson - Constructing variations of Hodge structure using Yang-Mills theory and application to uniformization, J. Amer. Math. Soc. 1 (1988), p. 867-918. | MR | Zbl | DOI

[52] C. Simpson, Harmonic bundles on non-compact curves, J. Amer. Math. Soc. 3 (1990), p. 713-770. | MR | Zbl | DOI

[53] C. Simpson, Mixed twistor structures, math. AG/9705006.

[54] C. Simpson, The Hodge filtration on nonabelian cohomology, in Algebraic geometry (Santa Cruz 1995), Proc. Sympos. Pure Math., vol. 62, Amer. Math. Soc., Providence, RI, 1997, p. 217-281. | MR | Zbl | DOI

[55] C. Simpson, Higgs bundles and local systems, Publ. Math. I.H.É.S. 75 (1992), p. 5-95. | MR | EuDML | Zbl | Numdam | DOI

[56] C. Simpson, Moduli of representations of the fundamental group of a smooth projective variety, I, Publ. Math. I.H.É.S. 79 (1994), p. 47-129. | MR | EuDML | Zbl | Numdam | DOI

[57] C. Simpson, Moduli of representations of the fundamental group of a smooth projective variety, II, Publ. Math. I.H.É.S. 80 (1994), p. 5-79. | MR | EuDML | Numdam | Zbl | DOI

[58] C. Simpson, private communication, 2003, fall.

[59] C. Simpson, Formalized proof, computation, and the construction problem in algebraic geometry, math.AG/0410224. | Zbl

[60] Y. T. Siu & G. Trautmann - Gap-sheaves and extension of coherent analytic subsheaves, Lecture Notes in Math., vol. 172, Springer-Verlag, Berlin-New York, 1971. | MR | Zbl

[61] Y. T. Siu - Techniques of extension of analytic objects, Lecture Notes in Pure and Appl. Math., vol. 8, Marcel Dekker, Inc., New York, 1974. | MR

[62] B. Steer & A. Wren The Donaldson-Hitchin-Kobayashi correspondence for parabolic bundles over orbifold surfaces, Canad. J. Math. 53 (2001), p. 1309-1339. | MR | Zbl | DOI

[63] K. Uhlenbeck - Connections with $L^{p}$ bounds on curvature, Comm. Math. Phys. 83 (1982), p. 31-42. | MR | Zbl | DOI

[64] K. Uhlenbeck & S. T. Yau - On the existence of Hermitian Yang-Mills connections in stable bundles, Comm. Pure Appl. Math. 39 (1986), p. 257-293. | MR | Zbl | DOI

[65] K. Yokogawa - Compactification of moduli of parabolic sheaves and moduli of parabolic Higgs sheaves, J. Math. Kyoto Univ. 33 (1993), p. 451-504. | MR | Zbl | DOI

[66] S. Zucker - Hodge theory with degenerating coefficients : $L^{2}$ cohomology in the Poincaré metric, Ann. of Math. 109 (1979), p. 415-476. | MR | Zbl | DOI

[67] K. Zuo - Representations of fundamental groups of algebraic varieties, Lecture Notes in Math., vol. 1708, Springer-Verlag, Berlin, 1999. | MR | Zbl