Universal parabolic moduli over $\overline{M}_{_{g, n}}$

TL;DR

This paper constructs a universal moduli space of stable parabolic vector bundles over the Deligne-Mumford moduli space of stable curves, ensuring well-behaved singularities and boundary objects.

Contribution

It introduces a universal moduli space of stable parabolic bundles over $ar{M}_{g,n}$ that includes boundary singularities as vector bundles, with good singularity properties.

Findings

Successful construction of the universal moduli space.

Boundary objects remain vector bundles.

Total space and fibers have good singularities.

Abstract

In this article we will construct a universal moduli space of stable parabolic vector bundles over the moduli space of marked Deligne-Mumford stable curves $\overline{M}_{_{g, n}}$. The objects that appear over the boundary of $\overline{M}_{_{g, n}}$ i.e., over singular curves will remain vector bundles. The total space and the fibers over $\overline{M}_{_{g, n}}$ will have good singularities.