Geometry Seminar

 

University of Tor Vergata, Department of Mathematics

18th of February 2025, 14:30-16:00,room D’Antoni

 

 

 

 

 

 

 

Distinguishing algebraic spaces from schemes

 

Dario Weissmann

IMPAN, Warsaw

 

 

 

 

We introduce local invariants of algebraic spaces and stacks which measure how far they are from being a scheme. Using these invariants, we develop mostly topological criteria to determine when the moduli space of a stack is a scheme. In the setting of a stack admitting a separated (good) moduli space this also yields a criterion for when the moduli space is a scheme. As an application we identify all separated good moduli spaces of vector bundles over a smooth projective curve which are schemes. This is joint work with Andres Fernandez Herrero and Xucheng Zhang.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This talk is part of the activity of the MIUR Excellence Department Projects MathMod@TOV, and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures