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SUMMARY:Quasi-projective stacks and ample vector bundles - Rachel Webb (Co
 rnell University)
DTSTART:20240618T090000Z
DTEND:20240618T100000Z
UID:TALK217672@talks.cam.ac.uk
DESCRIPTION:Ample line bundles on schemes have many equivalent characteriz
 ations\, but one key feature is that they can be used to embed the base sc
 heme into a projective space. I will present two natural definitions of an
  ample vector bundle on a stack\, not clearly equivalent\, one generalizin
 g a cohomological property and the other generalizing the embedding proper
 ty of ample line bundles. Using the latter\, and extending work of Kresch\
 , I will explain how an ample vector bundle on a tame stack induces an emb
 edding into [V^s/GL_r] where V^s is the twisted affine GIT stable locus in
  some polynomial representation V of GL_r. An application is the construct
 ion of moduli of stacks with ample vector bundle and in particular a very 
 general stack of tame stacky curves. This is joint with Daniel Bragg and M
 artin Olsson.
LOCATION:Seminar Room 1\, Newton Institute
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