Upcoming events

EDGE: Eric Ahlqvist (Edinburgh) -- Building data for stacky covers

Description: In this talk, I will define "stacky covers" — a class of stacks which contains flat root stacks and flat stacky modifications. These constructions naturally appear in Gromov–Witten theory, birational geometry, compactification of tame Deligne–Mumford stacks, and the theory of parabolic vector bundles among other fields.

Inspired by Pardini’s work in the 90s on abelian covers of algebraic varieties, I will show how to classify stacky covers in terms of certain intrinsically defined "building data". It turns out that a stacky cover can always be realized as the stack classifying trivializing 1-cochains of a certain 2-cocycle with values in a symmetric monoidal category. This approach not only sheds light on their structural properties but could also enhance our understanding of their role in broader mathematical contexts.

In the interest of time, I will also discuss an application of this theory towards reformulating Hurwitz's old problem of realizing ramified coverings with prescribed branch datum, specifically as a problem of realizing certain parabolic vector bundles with specific restrictions on their weights.