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Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization
Author(s):
Carlos T.
Simpson
Journal:
J. Amer. Math. Soc.
1
(1988),
867-918.
MSC:
Primary 58E15;
Secondary 32L15, 53C25, 53C55
MathSciNet review:
944577
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References:
-
- [1]
- L. V. Ahlfors, An extension of Schwarz's lemma, Trans. Amer. Math. Soc. 43 (1938), 359-364. MR 1501949
- [2]
- T. Aubin, Sur la fonction exponentielle, C. R. Acad. Sci. Paris 270A (1970), 1514-1516. MR 0271870 (42:6751)
- [3]
- K. Corlette, Flat
-bundles with canonical metrics, J. Differential Geom. (to appear). MR 965220 (89k:58066) - [4]
- M. Cornalba and P. Griffiths, Analytic cycles and vector bundles on non-compact algebraic varieties, Invent. Math. 28 (1975), 1-106. MR 0367263 (51:3505)
- [5]
- P. Deligne, Un théorème de finitude pour la monodromie, Discrete Groups in Geometry and Analysis, Birkhauser, Boston, 1987, pp. 1-19. MR 900821 (88h:14013)
- [6]
- P. Deligne and J. Milne, Tannakian categories, Lecture Notes in Math., no. 900, Springer, New York, 1982, 101-228.
- [7]
- S. K. Donaldson, Anti self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc. (3) 50 (1985), 1-26. MR 765366 (86h:58038)
- [8]
- S. K. Donaldson, Infinite determinants, stable bundles, and curvature, Duke Math. J. 54 (1987), 231-247. MR 885784 (88g:32046)
- [9]
- -, Twisted harmonic maps and the self-duality equations, Proc. London Math. Soc. (3) 55 (1987), 127-131. MR 887285 (88g:58040)
- [10]
- P. Griffiths, Periods of integrals on algebraic manifolds I, II, Amer. J. Math. 90 (1968); III, Inst. Hautes Études Sci. Publ. Math. 38 (1970).
- [11]
- P. Griffiths et al., Topics in transcendental algebraic geometry, Princeton Univ. Press, Princeton, NJ, 1984. MR 756842 (86b:14004)
- [12]
- P. Griffiths and W. Schmid, Locally homogeneous complex manifolds, Acta Math. 123 (1969), 253-302. MR 0259958 (41:4587)
- [13]
- R. S. Hamilton, Harmonic maps of manifolds with boundary, Lecture Notes in Math., no. 471, Springer, New York, 1975. MR 0482822 (58:2872)
- [14]
- N. J. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3) 55 (1987), 59-126. MR 887284 (89a:32021)
- [15]
- M. Kashiwara, Vanishing cycles and holonomic systems of differential equations, Lecture Notes in Math., no. 1016, Springer, New York, 1983, pp. 134-142. MR 726425 (85e:58137)
- [16]
- D. Kazhdan, On arithmetic varieties, Lie Groups and Their Representations, Halsted, New York, 1975. MR 0486316 (58:6073)
- [17]
- R. Kobayashi, Einstein-Kähler metrics on open algebraic surfaces of general type, Tohoku Math. J. 37 (1985), 43-77. MR 778371 (87a:53102)
- [18]
- S. Kobayashi and T. Ochiai, Holomorphic structures modeled after hyperquadrics, Tohoku Math. J. 34 (1982), 587-629. MR 685426 (84b:32039)
- [19]
- M. Lübke, Stability of Einstein-Hermitian vector bundles, Manuscripta Math. 42 (1983), 245-257. MR 701206 (85e:53087)
- [20]
- B. Malgrange, Polynôme de Bernstein-Sato et cohomologie évanescente, Astérisque 101-102 (1983), 243-267. MR 737934 (86f:58148)
- [21]
- Y. Miyaoka, On the Chern numbers of surfaces of general type, Invent. Math. 42 (1977), 225-237. MR 0460343 (57:337)
- [22]
- Y. Miyaoka, The maximal number of quotient singularities on surfaces with given numerical invariants, Math. Ann. 268 (1984), 159-171. MR 744605 (85j:14060)
- [23]
- C. C. Moore, Compactifications of symmetric spaces II: the Cartan domains, Amer. J. Math. 86 (1964), 358-378. MR 0161943 (28:5147)
- [24]
- D. Mumford and J. Fogarty, Geometric invariant theory, second ed., Springer-Verlag, New York, 1982. MR 719371 (86a:14006)
- [25]
- M. S. Narasimhan and C. S. Seshadri, Stable and unitary bundles on a compact Riemann surface, Ann. of Math. 82 (1965), 540-564. MR 0184252 (32:1725)
- [26]
- R. Palais, Foundations of global non-linear analysis, Benjamin, New York, 1968. MR 0248880 (40:2130)
- [27]
- W. Schmid, Variation of Hodge structure: the singularities of the period mapping, Invent. Math. 22 (1973), 211-319. MR 0382272 (52:3157)
- [28]
- B. Shiffman, Complete characterization of holomorphic chains of codimension one, Math. Ann. 274 (1986), 233-256. MR 838467 (87h:32022)
- [29]
- C. Simpson, Yang-Mills theory and uniformization, Lett. Math. Phys. 14 (1987), 371-377. MR 922832 (89a:32034)
- [30]
- K. K. Uhlenbeck and S. T. Yau, On the existence of Hermitian-Yang-Mills connections in stable vector bundles, Comm. Pure and Appl. Math. 39-S (1986), 257-293. MR 861491 (88i:58154)
- [31]
- S. T. Yau, Calabi's conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), no. 5, 1798-1799. MR 0451180 (56:9467)
- [32]
- A. Weil, Introduction à l'étude des variétés kähleriennes, Hermann, Paris, 1952.
- [33]
- S. Zucker, Hodge theory with degenerating coefficients:
cohomology in the Poincaré metric, Ann. of Math. 109 (1979), 415-476. MR 534758 (81a:14002) - [34]
- S. Kobayashi, Curvature and stability of vector bundles, Proc. Japan Acad. Ser. A 58 (1982), 158-162. MR 664562 (83i:53090)
- [35]
- M. Lübke, Chernklassen von Hermite-Einstein-Vektorbündeln, Math. Ann. 260 (1982), 133-141. MR 664372 (83m:32031)
- [36]
- V. B. Mehta and A. Ramanathan, Restriction of stable sheaves and representations of the fundamental group, Invent. Math. 77 (1984), 163-172. MR 751136 (85m:14026)
- [37]
- F. Takemoto, Stable vector bundles on algebraic surfaces, Nagoya Math. J. 47 (1972), 29-48. MR 0337966 (49:2735)
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Additional Information:
DOI:
10.1090/S0894-0347-1988-0944577-9
PII:
S0894-0347-1988-0944577-9
Copyright of article:
Copyright
1988,
American Mathematical Society
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