Moduli Stacks of Bundles on Local Surfaces

TL;DR

This paper provides an explicit description of stacks of vector bundles on formal neighborhoods of rational curves within algebraic surfaces, using a M"obius type automorphism group action.

Contribution

It introduces a novel groupoid presentation of these stacks, connecting automorphism groups with extension spaces in a new way.

Findings

Explicit groupoid presentation of vector bundle stacks

Identification of a M"obius type automorphism action

Enhanced understanding of bundle moduli on local surfaces

Abstract

We give an explicit groupoid presentation of certain stacks of vector bundles on formal neighborhoods of rational curves inside algebraic surfaces. The presentation involves a M\"obius type action of an automorphism group on a space of extensions.