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SUMMARY:Birational maps of Severi-Brauer surfaces\, with applications to C
 remona groups of higher rank
DTSTART:20220929T101500
DTEND:20220929T114500
DTSTAMP:20260506T170436Z
UID:569514a1df398724e7d8c22ded1ac96140beab2199c661af5cf6b4f2
CATEGORIES:Conferences - Seminars
DESCRIPTION:Julia Schneider (EPFL)\n\nThe Cremona group of rank N over a f
 ield K is the group of birational transformations of the projective N-spac
 e that are defined over K. In this talk\, however\, we will first focus o
 n birational transformations of (non-trivial) Severi-Brauersurfaces\, tha
 t is\, surfaces that become isomorphic to the projective plane over the 
 algebraic closure of K. In particular\, we will prove that if such a surfa
 ce contains a point of degree 6\, then its group of birational transforma
 tions is not generated by elementsof finite order as it admits a surjectiv
 e group homomorphism to the integers.\nAs an application\, we use this re
 sult to study Mori fiber spaces over the field of complex numbers\, for wh
 ich the generic fiber is a non-trivial Severi-Brauer surface. Weprove tha
 t any group of cardinality at most the one of the complex numbers is a qu
 otient of the Cremona group of rank 4 (and higher).\nThis is joint work in
  progress with Jérémy Blanc and Egor Yasinsky.
LOCATION:GR A3 32 https://plan.epfl.ch/?room==GR%20A3%2031
STATUS:CONFIRMED
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