The classification of semi-stable plane sheaves supported on sextic curves

TL;DR

This paper classifies semi-stable sheaves on the complex projective plane supported on sextic curves, providing geometric descriptions of their moduli space strata and decompositions.

Contribution

It offers a comprehensive classification of Gieseker semi-stable sheaves with multiplicity 6 on the projective plane, detailing their moduli space structure.

Findings

Decomposition of moduli spaces into natural strata

Concrete geometric descriptions of most strata

Explicit quotient descriptions of moduli space components

Abstract

We classify all Gieseker semi-stable sheaves on the complex projective plane that have dimension 1 and multiplicity 6. We decompose their moduli spaces into strata which occur naturally as quotients modulo actions of certain algebraic groups. In most cases we give concrete geometric descriptions of the strata.