*AVVISO SEMINARI DI MATEMATICA*
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Data: mercoledì 4 MARZO 2020
Luogo: Aula Magna del Dipartimento di Matematica di Pisa
Programma:
15:00--16:00 David Rydh (Stockholm): Derived blow-ups and deformation to
the normal cone
Abstract: I will describe the functor of points of blow-ups and
deformations to the normal cone using derived algebraic geometry. One
application is a natural and easy construction of virtual fundamental
classes and virtual pull-backs. Another potential application is to Kirwan
partial desingularization and the generalized DT-invariants recently
constructed by Kiem, Li and Savvas. This is joint work with A. Khan.
16:00--16:30 Coffee break
16:30--17:30 Roberto Pirisi (Stockholm): Brauer groups of moduli of
hyperelliptic curves, via cohomological invariants
Abstract: We use the theory of cohomological invariants for algebraic
stacks to completely describe the Brauer group of the moduli stacks H_g of
genus g hyperellitic curves over fields of characteristic zero, and the
prime-to-char(k) part in positive characteristic. It turns out that the
(non-trivial part of the) group is generated by cyclic algebras, by an
element coming from a map to the classifying stack of étale algebras of
degree 2g+2, and when g is odd by the Brauer-Severi fibration induced by
taking the quotient of the universal curve by the hyperelliptic involution.
This paints a richer picture than in the case of elliptic curves, where all
non-trivial elements come from cyclic algebras. This is joint work with
Andrea di Lorenzo.
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