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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.