On two notions of semistability

Mario Maican

Vol. 234 (2008), No. 1, 69–135

DOI: 10.2140/pjm.2008.234.69

Abstract

We show that certain semistable sheaves on the projective plane with linear Hilbert polynomial are cokernels of semistable morphisms of decomposable bundles. We exhibit certain locally closed subvarieties or open dense subsets of moduli spaces of semistable sheaves as quotients modulo nonreductive groups. These subvarieties are defined by cohomological conditions. We find isomorphisms between such subvarieties given by sending a sheaf to its dual.

Keywords

moduli spaces, nonreductive groups, sheaves on the projective plane, semistable sheaves, sheaves of dimension one

Mathematical Subject Classification 2000

Primary: 14F05, 14L24, 00A05, 14D20, 14D22

Milestones

Received: 14 May 2007

Revised: 19 October 2007

Accepted: 22 October 2007

Published: 1 January 2008