Moduli of vector bundles, Frobenius splitting, and invariant theory

• 成果类型: Article
• 署名作者: Mehta, VB; Ramadas, TR
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/2118593
• 发表日期: 1996
• 页码: 269-313
• 关键词: varieties; sheaves; CURVES

摘要

Let X be an irreducible projective curve of genus g over an algebraically closed field of positive characteristic not equal 2, 3. In Part I, we prove, adapting the degeneration arguments of [N-TR], that moduli spaces of rank-two (parabolic) bundles on X are Frobenius split [M-R] for generic smooth X. (A similar result holds for X nodal. A consequence is the Verlinde formula in positive characteristic.) In Part II, we give a direct proof of the fact that the local rings of the moduli spaces are F-split, and further, that they are Cohen-Macaulay. This involves showing that the ring of invariants of g copies of 2 x 2 matrices (under the adjoint action of SL(2)) is F-split and Cohen-Macaulay.