A Duality Result for Moduli Spaces of Semistable Sheaves Supported on Projective Curves

TL;DR

This paper proves a duality isomorphism between moduli spaces of semistable sheaves on projective space with support on curves, relating sheaves with Euler characteristic c to those with -c.

Contribution

It establishes a new duality result linking moduli spaces of semistable sheaves with opposite Euler characteristics on projective space.

Findings

Moduli space M(r,c) is isomorphic to M(r,-c).

Duality provides a symmetry in the classification of sheaves.

Results apply to sheaves supported on curves in projective space.

Abstract

We show that the moduli space M(r,c) of semistable sheaves on n-dimensional projective space with support of dimension one, with multiplicity r and with Euler characteristic c is isomorphic to M(r,-c).