On the Euler numbers of certain moduli spaces of curves and points

TL;DR

This paper computes the topological Euler numbers of specific moduli spaces of curves and points in smooth projective varieties using virtual Hodge polynomials and torus actions, with implications for Donaldson-Thomas invariants.

Contribution

It introduces a method to determine Euler numbers of certain moduli spaces via virtual Hodge polynomials and torus actions, connecting to Donaldson-Thomas invariants.

Findings

Euler numbers of moduli spaces are explicitly computed.

The approach involves virtual Hodge polynomials and torus actions.

Results provide insights into Donaldson-Thomas invariants.

Abstract

We determine the topological Euler number of certain moduli space of 1-dimensional closed subschemes in a smooth projective variety which admits a Zariski-locally trivial fibration with 1-dimensional fibers. The main approach is to use virtual Hodge polynomials and torus actions. The results might shed some light on the corresponding Donaldson-Thomas invariants.