@book{AST_2006__309__R1_0,
author = {Takuro, Mochizuki},
title = {Kobayashi-Hitchin correspondence for tame harmonic bundles and an application},
series = {Ast\'erisque},
year = {2006},
publisher = {Soci\'et\'e math\'ematique de France},
number = {309},
mrnumber = {2310103},
zbl = {1119.14001},
language = {en},
url = {https://www.numdam.org/item/AST_2006__309__R1_0/}
}
Takuro, Mochizuki. Kobayashi-Hitchin correspondence for tame harmonic bundles and an application. Astérisque, no. 309 (2006), 125 p. https://www.numdam.org/item/AST_2006__309__R1_0/
[1] - An extension of Schwarz's lemma, Trans. Amer. Math. Soc. 43 (1938), p. 359-364. | MR | JFM
[2] & - 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] - Nonlinear analysis on manifolds. Monge-Ampère equations, Springer-Verlag, Berlin-New York, 1982. | MR | Zbl
[4] - Sur les fibrés paraboliques sur une surface complexe, J. London Math. Soc. 53 (1996), no. 2, p. 302-316. | MR | Zbl | DOI
[5] , 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] - Flat -bundles with canonical metrics, J. Differential Geom. 28 (1988), p. 361-382. | MR | Zbl | DOI
[7] , 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] & - Analytic cycles and vector bundles on non-compact algebraic varieties, Invent. Math. 28 (1975), p. 1-106. | MR | EuDML | Zbl | DOI
[9] - Équations différentielles à points singuliers réguliers, Lecture Notes in Math., vol. 163, Springer-Verlag, Berlin-New York, 1970. | MR | Zbl
[10] , Un théorème de finitude pour la monodromie, in Discrete Groups in Geometry and Analysis, Birkhäuser, 1987, p. 1-19. | MR | Zbl
[11] , , & - Hodge cycles, motives, and Shimura varieties, Lecture Notes in Math., vol. 900, Springer-Verlag, Berlin-New York, 1982. | MR | Zbl
[12] - A new proof of a theorem of Narasimhan and Seshadri, J. Differential Geom. 18 (1983), p. 269-277. | MR | Zbl | DOI
[13] , 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] , Infinite determinants, stable bundles and curvature, Duke Math. J. 54 (1987), p. 231-247. | MR | Zbl | DOI
[15] , Twisted harmonic maps and the self-duality equations, Proc. London Math. Soc. 55 (1987), p. 127-131. | MR | Zbl | DOI
[16] The gauge theory and topology, Springer-Verlag, Tokyo, 1995, in Japanese.
[17] - Intersection theory, second ed., Springer-Verlag, Berlin, 1988. | MR
[18] & - Elliptic partial differential equations of second order, second ed., Springer-Verlag, Berlin, 1983. | MR | Zbl | DOI
[19] - 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] - Algebraic geometry, Springer-Verlag, New York-Heidelberg, 1977. | MR | Zbl | DOI
[21] , Stable reflexive sheaves, Math. Ann. 254 (1980), p. 121-176. | MR | EuDML | Zbl | DOI
[23] - The structure of Lie groups, Holden-Day, 1965. | MR
[24] - An introduction to complex analysis in several variables, North-Holland Publishing Co., Amsterdam, 1990. | MR | Zbl
[25] & - Framed modules and their moduli, Internat. J. Math. 6 (1995), p. 297-324. | MR | Zbl | DOI
[26] - Functional Analysis, Iwanami Shoten, Tokyo, 1983, in Japanese. | MR
[27] & - A relation between the parabolic Chern characters of the de Rham bundles, math. AG/0603677. | MR | Zbl
[28] , & - Harmonic bundles on quasi-compact Kaehler manifolds, math.AG/0108166.
[29] & - 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] - First Chern class and holomorphic tensor fields, Nagoya Math. J. 77 (1980), p. 5-11. | MR | Zbl | DOI
[31] , Curvature and stability of vector bundles, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), p. 158-162. | MR | Zbl | DOI
[32] , Differential geometry of complex vector bundles, Princeton University Press/Iwanami Shoten, Princeton, NJ/Tokyo, 1987. | MR | Zbl | DOI
[33] - Valuative criteria for families of vector bundles on algebraic varieties, Ann. of Math. 101 (1975), p. 88-110. | MR | Zbl | DOI
[34] - Hitchin's self-duality equations on complete Riemannian manifolds, Math. Ann. 306 (1996), p. 419-428. | MR | EuDML | Zbl | DOI
[35] , 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] & - Hermitian-Einstein metrics on parabolic stable bundles, Acta Math. Sin. (Engl. Ser.) 15 (1999), p. 93-114. | MR | Zbl | DOI
[37] - Stability of Einstein-Hermitian vector bundles, Manuscripta Math. 42 (1983), p. 245-257. | MR | EuDML | Zbl | DOI
[38] & - The universal Kobayashi-Hitchin correspondence on Hermitian manifolds, math.DG/0402341, to appear in Mem. Amer. Math. Soc. | Zbl | MR | DOI
[39] & - Moduli of parabolic stable sheaves, Math. Ann. 293 (1992), p. 77-99. | MR | EuDML | Zbl | DOI
[40] & Restriction of stable sheaves and representations of the fundamental group, Invent. Math. 77 (1984), p. 163-172. | MR | EuDML | Zbl | DOI
[41] & , Semistable sheaves on projective varieties and their restriction to curves, Math. Ann. 258 (1982), p. 213-224. | MR | EuDML | Zbl | DOI
[42] & - Moduli of vector bundles on curves with parabolic structures, Math. Ann. 248 (1980), p. 205-239. | MR | EuDML | Zbl | DOI
[43] - Asymptotic behaviour of tame nilpotent harmonic bundles with trivial parabolic structure, J. Differential Geom. 62 (2002), p. 351-559. | MR | Zbl | DOI
[44] , 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] , A characterization of semisimple local system by tame pure imaginary pluri-harmonic metric, math.DG/0402122, to appear as a part of [44].
[46] , Kobayahi-Hitchin correspondence for tame harmonic bundles and an application II, math.DG/0602266.
[47] & Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math. 82 (1965), p. 540-567. | MR | Zbl | DOI
[48] - Foundations of global non-linear analysis, Benjamin, 1968. | MR | Zbl
[49] - Parabolic vector bundles and Hermitian-Yang-Mills connections over a Riemann surface, Internat. J. Math. 4 (1993), p. 467-501. | MR | Zbl | DOI
[50] - Polarizable twistor -modules, Astérisque, vol. 300, Soc. Math. France, Paris, 2005. | MR | Zbl | Numdam
[51] - 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] , Harmonic bundles on non-compact curves, J. Amer. Math. Soc. 3 (1990), p. 713-770. | MR | Zbl | DOI
[53] , Mixed twistor structures, math. AG/9705006.
[54] , 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] , Higgs bundles and local systems, Publ. Math. I.H.É.S. 75 (1992), p. 5-95. | MR | EuDML | Zbl | Numdam | DOI
[56] , 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] , 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] , private communication, 2003, fall.
[59] , Formalized proof, computation, and the construction problem in algebraic geometry, math.AG/0410224. | Zbl
[60] & - Gap-sheaves and extension of coherent analytic subsheaves, Lecture Notes in Math., vol. 172, Springer-Verlag, Berlin-New York, 1971. | MR | Zbl
[61] - Techniques of extension of analytic objects, Lecture Notes in Pure and Appl. Math., vol. 8, Marcel Dekker, Inc., New York, 1974. | MR
[62] & The Donaldson-Hitchin-Kobayashi correspondence for parabolic bundles over orbifold surfaces, Canad. J. Math. 53 (2001), p. 1309-1339. | MR | Zbl | DOI
[63] - Connections with bounds on curvature, Comm. Math. Phys. 83 (1982), p. 31-42. | MR | Zbl | DOI
[64] & - On the existence of Hermitian Yang-Mills connections in stable bundles, Comm. Pure Appl. Math. 39 (1986), p. 257-293. | MR | Zbl | DOI
[65] - 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] - Hodge theory with degenerating coefficients : cohomology in the Poincaré metric, Ann. of Math. 109 (1979), p. 415-476. | MR | Zbl | DOI
[67] - Representations of fundamental groups of algebraic varieties, Lecture Notes in Math., vol. 1708, Springer-Verlag, Berlin, 1999. | MR | Zbl






