On the moduli of stable sheaves on some nonreduced projective schemes

Abstract

We study the moduli space of stable sheaves on a projective scheme whose structure sheaf has a nilpotent ideal with some property. We introduce a stratification on this moduli space. Each stratum is the moduli space of some extensions of sheaves. This stratification is described on a curve with multiple structure and on a double plane, and the structure of each stratum is studied. In the case of a curve with multiple structure, we also study a local structure of the moduli space of stable sheaves.