论文信息 - Holomorphic principal bundles over elliptic curves

Holomorphic principal bundles over elliptic curves

In this paper, the first of a series of three, we classify holomorphic principal G-bundles over an elliptic curve, where G is a reductive group. We also study the local and global properties of the moduli space of semistable G-bundles. We identify canonical representatives for each S-equivalence class of semistable G-bundles, and study their automorphism groups.

J. Morgan | R. Friedman

[1] A. Ramanathan. Moduli for principal bundles over algebraic curves: II , 1996 .

[2] R. Friedman. Vector bundles and (3)-invariants for elliptic surfaces , 1995 .

[3] A. Beauville,et al. Conformal blocks and generalized theta functions , 1993, alg-geom/9309003.

[4] R. Friedman. Rank two vector bundles over regular elliptic surfaces , 1989 .

[5] Raoul Bott,et al. The Yang-Mills equations over Riemann surfaces , 1983, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[6] S. Donaldson,et al. A new proof of a theorem of Narasimhan and Seshadri , 1983 .

[7] O. Shvartsman,et al. Chevalley's theorem for complex crystallographic Coxeter groups , 1978 .

[8] E. Looijenga. Root systems and elliptic curves , 1976 .

[9] A. Ramanathan. Stable principal bundles on a compact Riemann surface , 1975 .

[10] C. S. Seshadri,et al. STABLE BUNDLES AND UNITARY BUNDLES ON A COMPACT RIEMANN SURFACE. , 1964, Proceedings of the National Academy of Sciences of the United States of America.

[11] B. Kostant,et al. The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group , 1959 .

[12] Michael Atiyah,et al. Vector Bundles Over an Elliptic Curve , 1957 .