Geometric invariant theory and flips

• 成果类型: Article
• 署名作者: Thaddeus, M
• 刊物名称: JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY
• ISSN/ISSBN: 0894-0347
• DOI: 10.1090/S0894-0347-96-00204-4
• 发表日期: 1996
• 页码: 691-723
• 关键词: reduced phase-space; vector-bundles; algebraic groups; symplectic form; co-homology; CURVES; MODULI; VARIETIES

摘要

We study the dependence of geometric invariant theory quotients on the choice of a linearization. We show that, in good cases, two such quotients are related by a flip in the sense of Mori, and explain the relationship with the minimal model program. Moreover, we express the flip as the blow-up and blow-down of specific ideal sheaves, leading, under certain hypotheses, to a quite explicit description of the flip. We apply these ideas to various familiar moduli problems, recovering results of Kirwan, Boden-Hu, Bertram-Daskalopoulos-Wentworth, and the author. Along the way we display a chamber structure, following Duistermaat-Heckman, on the, space of all linearizations. We also give a new, easy proof of the Bialynicki-Birula decomposition theorem.