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SUMMARY:Del Pezzo surfaces with global vector fields
DTSTART:20250417T120000Z
DTEND:20250417T140000Z
DTSTAMP:20260504T230000Z
UID:indico-event-14008@indico.math.cnrs.fr
DESCRIPTION:Speakers: Claudia Stadlmayr\n\nIf X is a del Pezzo surface (or
  a weak del Pezzo\, or an RDP del Pezzo)\, then its automorphism scheme Au
 t_X is a\, possibly non-reduced\, affine group scheme of finite type. In p
 articular\, X has infinitely many automorphisms if and only if Aut_X is po
 sitive-dimensional and then X admits global vector fields (since the space
  of global vector fields on X is the tangent space to the automorphism sch
 eme). The last implication is an equivalence in characteristic 0\, but its
  converse can fail in positive characteristic. Over the complex numbers\, 
 a del Pezzo surface with rational double point singularities admits global
  vector fields if and only if its minimal resolution\, the corresponding w
 eak del Pezzo surface\, does. In small characteristics\, one implication o
 f this equivalence breaks down due to the existence of non-lifting vector 
 fields on rational double points. I will explain how to overcome these obs
 tacles in order to classify weak and RDP (if p \\neq 2) del Pezzo surfaces
  with global vector fields. Further\, I will show examples of such surface
 s displaying interesting behaviour in small characteristics. This is joint
  work with G. Martin.\n \n\nhttps://indico.math.cnrs.fr/event/14008/
URL:https://indico.math.cnrs.fr/event/14008/
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