SEMINARIO
DI MATEMATICA
ore 15.00
Scuola Normale
Superiore
Pisa
(Sala degli
Stemmi)
Gabriele
Vezzosi
Université
de Lille - France
Terrà un seminario dal
titolo:
“Reduced
obstruction theories via derived algebraic geometry”
Abstract
Let S
be an algebraic K3-surface, g ≥ 0, and b ≠ 0 in H_2(S, Z) a curve class. After
recalling the necessary background on derived algebraic geometry I will
construct a derived stack RM whose truncation is the usual stack M of stable
maps from curves of genus g to S hitting the class b, and such that the
inclusion of M into RM induces on M a perfect obstruction theory whose tangent
and obstruction spaces coincide with the corresponding reduced spaces of
Okounkov–Maulik–Pandharipande–Thomas. This approach uses derived algebraic
geometry and yields not only a full rigorous proof of the existence of a global
reduced obstruction theory, not relying on any result on semiregularity maps,
but also a new global geometric interpretation. This is joint work with T.
Schürg (Mainz) and B. Toën (CNRS, Montpellier).
Tutti gli
interessati sono invitati a partecipare.
Classe
di Scienze