Direct image and pullback of Parabolic vector bundles

TL;DR

This paper explores the correspondence between parabolic vector bundles on curves and vector bundles on root stacks, focusing on direct image and pullback operations, and discusses their applications.

Contribution

It establishes that direct image and pullback of parabolic bundles correspond to similar operations on root stacks, clarifying their relationship.

Findings

Direct image of parabolic bundles corresponds to direct image on root stacks.

Pullback of parabolic bundles corresponds to pullback on root stacks.

Applications of this correspondence are demonstrated.

Abstract

Niels Borne established a natural correspondence between the parabolic vector bundles on curves and vector bundles on root stacks. The notions of direct image of parabolic vector bundles and pullback of parabolic vector bundles were studied in \cite{Alfaya_Biswas}. We show that these two notions correspond to the notions direct image of vector bundles on root stacks and pullback of vector bundles on root stacks respectively. Some applications of this correspondence are given.