On the geometry of the moduli space of semi-stable plane sheaves with Hilbert polynomial P(m)=6m+3

TL;DR

This paper classifies semi-stable sheaves on the complex projective plane with specific invariants and explores the geometric structure of their moduli space, revealing a birational relationship to a blow-up of a moduli space of Kronecker modules.

Contribution

It provides a complete classification of these sheaves and describes the geometry of their moduli space in relation to Kronecker modules.

Findings

Moduli space is birational to a blow-up of a Kronecker module moduli space.

Complete classification of semi-stable sheaves with given invariants.

Identification of the geometric structure of the moduli space.

Abstract

We classify all Gieseker semi-stable sheaves on the complex projective plane that have dimension 1, multiplicity 6 and Euler characteristic 3. We show that their moduli space is birational to the blow-up at a special point of a certain moduli space of semi-stable Kronecker modules.