10 research outputs found
A functorial construction of moduli of sheaves
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.Comment: 52 pp. Dedicated to the memory of Joseph Le Potier. To appear in
Inventiones Mathematicae. Slight change in the definition of the Kronecker
algebra in Secs 1 (p3) and 2.2 (p6), with corresponding small alterations
elsewhere, to make the constructions work for non-reduced schemes. Section
6.5 rewritten. Remark 2.6 and new references adde