Seminário de Geometria Algébrica e Geometria Complexa – Michele Graffeo (SISSA) em 29/09 e Sokratis Zikas (IMPA) em 02/10 – 14h30
Esta semana teremos duas sessões do nosso Seminário de Geometria Algébrica e Geometria Complexa da UFF, nos dias 20/09 e 02/10, ambas às 14h30, na sala 407 – Bloco H – Campus do Gragoatá.
Na 2a-feira dia 29/09 teremos Michele Graffeo (SISSA):Título: New components of Hilbert schemes of points and 2-step ideals
Resumo: Hilbert schemes of points on a quasi-projective variety X are classical objects in algebraic geometry. Roughly speaking, they parametrise ideals of a polynomial ring with complex coefficients having finite colength. Although Hilbert schemes always have a distinguished component called the smoothable component, their geometry is quite pathological and one of the main open problems around them concerns their irreducibility. In a joint work with Giovenzana, Giovenzana, Lella we introduce the notion of 2-step ideals. We show that the loci parametrising these ideals are in general not contained in the smoothable component of the Hilbert scheme, thus providing new examples of extra-components. In my seminar I will discuss our class of ideals and relate them to the compressed algebras considered by Iarrobbino in the eighties. Finally, I will show how to extend our result to the nested setting.
Na 5a-feira dia 02/10 teremos Sokratis Zikas (IMPA):
Título: On Mori Dreamness of blowups along space curves
Resumo: Mori Dream Spaces are a special kind of varieties introduced by Hu and Keel that enjoy very good properties with respect to Mori theory. While Mori Dreamness is a very desirable property, it is not very well behaved with respect to even the simplest birational maps: blowups. In this talk we study Mori Dreamness of blowups along space curves: we provide various sufficient criteria as well obstructions to the blowup being a Mori Dream Space. We also study how this property changes while varying the curve in the corresponding Hilbert scheme, exhibiting various degenerational pathologies. This is joint work with Tiago Duarte Guerreiro.
Para maiores informações sobre os próximos seminários e o histórico, basta consultar o site: https://sites.google.com/view/geoalgcompluff
Atenciosamente,
Juliana Coelho
Nivaldo Medeiros
Viviana Ferrer
