Seminário de Geometria Algébrica da UFF – Daniela Paiva – 05/05

Convidamos a tod@s para participar de mais uma edição do Seminário de Geometria Algébrica da UFF!

Palestrante: Daniela Paiva Peñuela (IMPA)
Data: 05/05 Horário: 16h Sala: 407 – Bloco H – Gragoatá

Title: On the Gizatullin problem.

Abstract: K3 surfaces are characterized by having a nowhere vanishing rational 2-form and irregularity equal to zero. Smooth quartic surfaces in ℙ³ are such surfaces. Given a smooth quartic K3 surface S ⊂ ℙ³,Gizatullin was interested in which automorphisms of S are induced by Cremona transformations of ℙ³. Later on, Oguiso answered it for some interesting examples and he posed the following natural question:

Is every automorphism of finite order of any smooth quartic surface S ⊂ ℙ³ induced by a Cremona transformation?

In this talk, we will give a negative answer to this question by constructing a smooth quartic K3 surfaces S with Picard number two such that Aut(S) = D∞ together with an involution of S that is not derived by any element of Bir(ℙ³). More precisely, we will prove that no element of Aut(S) is induced by an element of Bir(ℙ³). This is joint work with Ana Vitoria M Quedo.