Relative Hilbert schemes and moduli spaces of torsion plane sheaves

TL;DR

This paper explores the connections between flag Hilbert schemes of points on plane curves and moduli spaces of one-dimensional plane sheaves, revealing their unirationality in certain cases.

Contribution

It establishes relations between flag Hilbert schemes and moduli spaces of plane sheaves, demonstrating the unirationality of some moduli spaces.

Findings

Relations between flag Hilbert schemes and moduli spaces established

Some moduli spaces shown to be unirational

Contributes to understanding of plane sheaves and Hilbert schemes

Abstract

We find certain relations between flag Hilbert schemes of points on plane curves and moduli spaces of one-dimensional plane sheaves. We show that some of these moduli spaces are unirational.