MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations

• 成果类型: Article
• 署名作者: Bayer, Arend; Macri, Emanuele
• 署名单位: University of Edinburgh; University System of Ohio; Ohio State University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0501-8
• 发表日期: 2014
• 页码: 505-590
• 关键词: compact hyperkahler manifolds; stability conditions; rational curves; hilbert schemes; t-structures; SPACES; VARIETIES; SURFACES; equivalences; INVARIANTS

摘要

We use wall-crossing with respect to Bridgeland stability conditions to systematically study the birational geometry of a moduli space of stable sheaves on a K3 surface : (a) We describe the nef cone, the movable cone, and the effective cone of in terms of the Mukai lattice of . (b) We establish a long-standing conjecture that predicts the existence of a birational Lagrangian fibration on whenever admits an integral divisor class of square zero (with respect to the Beauville-Bogomolov form). These results are proved using a natural map from the space of Bridgeland stability conditions to the cone of movable divisors on ; this map relates wall-crossing in to birational transformations of . In particular, every minimal model of appears as a moduli space of Bridgeland-stable objects on .