Cohomology of Moduli Stacks of Principal $\Bbb C^*$-Bundles Over Nodal Algebraic Curves

TL;DR

This paper computes the rational cohomology of moduli stacks of principal complex line bundles over nodal algebraic curves, revealing their algebraic structure in terms of Chern classes.

Contribution

It provides a detailed description of the rational cohomology algebra of these moduli stacks, a novel result in the context of nodal curves.

Findings

Rational cohomology algebra expressed via Chern classes

Explicit computation for moduli stacks over nodal curves

Advances understanding of algebraic topology of moduli spaces

Abstract

We study moduli stacks of principal $\Bbb C^*$-bundles over nodal complex algebraic curves and determine their rational cohomology algebras in terms of Chern classes.