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VERSION:2.0
PRODID:-//Memento EPFL//
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SUMMARY:Automorphisms of smooth hypersurfaces and Gizatullin's problem
DTSTART:20250925T101500
DTEND:20250925T120000
DTSTAMP:20260506T195003Z
UID:5547f03bb6de13ad895e7d692327d6a92775d37e5bd8658c5594bd5c
CATEGORIES:Conferences - Seminars
DESCRIPTION:Sokratis Zikas\nLet $X_d \\subset \\mathbb{P}^{n+1}$ be a smoo
 th hypersurface of degree d. Classical theorems of Matsumura-Monsky and Ch
 ang state that every automorphism of $X_d$ is the restriction of a linear 
 automorphism of the ambient space\, except in the two exceptional cases (n
 \,d) = (1\,3) and (2\,4). Nonetheless\, when (n\,d) = (1\,3)\, every autom
 orphism of $X_3$ can be realized as the restriction of a birational map of
  $\\mathbb{P}^{2}$.  Gizatullin’s problem concerns the last open case\
 , i.e. which automorphisms of a smooth quartic surface $X_4 \\subset \\mat
 hbb{P}^{3}$ are restrictions of birational selfmaps of the ambient space.\
 nIn this talk we will employ the machinery of log Calabi-Yau pairs\, and m
 ore specifically that of the volume preserving Sarkisov program\, to compl
 etely address Gizatullin’s problem for the general non-trivial case: sm
 ooth quartics of Picard rank 2. We will see that the answer can be either 
 positive or negative\, the dependence being on the existence of certain cu
 rves on the quartic. This is joint work with Carolina Araujo and Daniela 
 Paiva.
LOCATION:CM 0 13
STATUS:CONFIRMED
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