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SUMMARY:Geometric helices on del Pezzo surfaces from tilting [Seminar Alge
 braic Geometry (SAG)]
DTSTART:20260702T083000Z
DTEND:20260702T093000Z
DTSTAMP:20260702T051600Z
UID:indico-event-1430@math-events.uni-bonn.de
DESCRIPTION:Speakers: Pierrick Bousseau (Oxford\, zZt MPI)\n\nGeometric he
 lices on a surface S are sequences of objects in the derived category of c
 oherent sheaves on S that provide a way to describe the derived category o
 f coherent sheaves on the local surface K_S​ in terms of a quiver with p
 otential.  We prove that all geometric helices in the derived category of
  coherent sheaves on a del Pezzo surface are related by a sequence of elem
 entary operations: rotation\, shifting\, orthogonal reordering\, tensoring
  by a line bundle\, and tilting. As a consequence\, any two non-commutativ
 e crepant resolutions of the affine cone over a del Pezzo surface are rela
 ted by mutations. The proof relies on a geometric interpretation of tiltin
 g operations as cluster transformations acting on toric models of a log Ca
 labi-Yau surface mirror to the del Pezzo surface.\n\nhttps://math-events.u
 ni-bonn.de/event/1430/
LOCATION:MPIM\, Vivatsgasse\,  7 - Seminar Room (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1430/
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