A functorial construction of moduli of sheaves

• 成果类型: Article
• 署名作者: Alvarez-Consul, Luis; King, Alastair
• 署名单位: Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT); University of Bath
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-007-0042-5
• 发表日期: 2007
• 页码: 613-666
• 关键词: stable vector-bundles; semistable sheaves; projective plane; semi-invariants; VARIETIES; families; QUIVERS; surface; SPACES

摘要

We show how natural functors from the category of coherent sheaves on a projective scheme to categories of Kronecker modules can be used to construct moduli spaces of semistable sheaves. This construction simplifies or clarifies technical aspects of existing constructions and yields new simpler definitions of theta functions, about which more complete results can be proved.