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SUMMARY:Carolina Araujo (IMPA)
DTSTART:20201208T141500Z
DTEND:20201208T151500Z
DTSTAMP:20260423T040007Z
UID:EDGE2020/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EDGE2020/5/"
 >Birational geometry of Calabi-Yau pairs and 3-dimensional Cremona transfo
 rmations</a>\nby Carolina Araujo (IMPA) as part of EDGE 2020 (online)\n\n\
 nAbstract\nRecently\, Oguiso addressed the following question\, attributed
  to Gizatullin: ``Which automorphisms of a smooth quartic K3 surface $D\\s
 ubset \\mathbb{P}^3$ are induced by Cremona transformations of the ambient
  space $\\mathbb{P}^3$?'' When $D\\subset \\mathbb{P}^3$  is a quartic sur
 face\, $(\\mathbb{P}^3\,D)$ is an example of a \\emph{Calabi-Yau pair}\, t
 hat is\, a pair $(X\,D)$\, consisting of a normal projective variety $X$ a
 nd an effective Weil divisor $D$ on $X$ such that $K_X+D\\sim 0$. Gizatull
 in's question is about birational properties of the Calabi-Yau pair $(\\ma
 thbb{P}^3\,D)$. In this talk\, I will explain a general framework to study
  the birational geometry of mildly singular Calabi-Yau pairs. Then I will 
 focus on the case of singular quartic surfaces $D\\subset \\mathbb{P}^3$. 
 Our results illustrate how the appearance of increasingly worse singularit
 ies in $D$ enriches the birational geometry of the pair $(\\mathbb{P}^3\, 
 D)$\, and lead to interesting subgroups of the Cremona group of $\\mathbb{
 P}^3$. This is joint work with Alessio Corti and Alex Massarenti.\n
LOCATION:https://researchseminars.org/talk/EDGE2020/5/
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