@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/} }
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/
[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
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