On the moduli space of semi-stable plane sheaves with Hilbert polynomial P(m)=6m+2

TL;DR

This paper investigates the structure of the moduli space of semi-stable sheaves on the complex projective plane with specific invariants, providing explicit descriptions and stratifications based on sheaf types.

Contribution

It offers a concrete description of these sheaves as cokernels of morphisms and stratifies the moduli space according to sheaf types, advancing understanding of their geometric structure.

Findings

Explicit description of sheaves as cokernels of morphisms

Stratification of the moduli space by sheaf types

Detailed geometric analysis of the moduli space

Abstract

We study the Simpson moduli space of semi-stable sheaves on the complex projective plane that have dimension 1, multiplicity 6 and Euler characteristic 2. We describe concretely these sheaves as cokernels of morphisms of locally free sheaves and we stratify the moduli space according to the types of sheaves that occur.