Geometry Seminar

 

University of Tor Vergata, Department of Mathematics

12^th  of March 2024, 14:30-16:00, room “Dal Passo”

 

 

 

 

 

 

 

The importance of being a weighted blow-up

 

 

 

 

Andrea Di Lorenzo
Università di Pisa

 

 

Blow-ups are fundamental tools in algebraic geometry, and there
are several results (e.g the famous Castelnuovo's theorem) that can be used
to determine when a variety is obtained as a blow-up of a smooth variety
along a smooth center. Weighted blow-ups play a similar role for stacks. In
this talk I will present a criterion for finding out if a smooth DM stack
is a weighted blow-up. I will apply this result for showing that certain
alternative compactifications of moduli of marked elliptic curves are
obtained via weighted blow-ups (and blow-downs). This in turn will prove to
be useful in order to compute certain invariants, like Chow rings or Brauer
groups. First part of this talk is a joint work with Arena, Inchiostro,
Mathur, Obinna and Pernice; the second part of this talk is a joint work
with L. Battistella.

 

 

 

 

 

 

 

 

 

 

 

 

This talk is part of the activity of the MIUR Excellence Department Projects MathMod@TOV, and the PRIN 2022 Moduli Spaces and Birational Geometry