Hodge polynomials and birational types of moduli spaces of coherent systems on elliptic curves

TL;DR

This paper computes Hodge polynomials and determines the birational types of moduli spaces of coherent systems on elliptic curves, revealing isomorphisms via Fourier-Mukai transforms.

Contribution

It introduces methods to compute Hodge polynomials and classify birational types of these moduli spaces, including establishing isomorphisms using Fourier-Mukai transforms.

Findings

Computed Hodge polynomials of moduli spaces

Determined birational types in specific cases

Proved isomorphisms between certain moduli spaces

Abstract

In this paper we consider moduli spaces of coherent systems on an elliptic curve. We compute their Hodge polynomials and determine their birational types in some cases. Moreover we prove that certain moduli spaces of coherent systems are isomorphic. This last result uses the Fourier-Mukai transform of coherent systems introduced by Hern\'andez Ruiperez and Tejero Prieto.