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SUMMARY:Compactified Universal Jacobians via Geometric Invariant Theory - 
 George Cooper (University of Oxford)
DTSTART:20240117T120000Z
DTEND:20240117T124500Z
UID:TALK210613@talks.cam.ac.uk
DESCRIPTION:Associated to any smooth projective curve $C$ is its degree $d
 $ Jacobian variety\, parametrising isomorphism classes of degree $d$ line 
 bundles on $C$. Letting the curve vary as well\, one is led to the univers
 al Jacobian stack. This stack admits several compactifications over the st
 ack of marked stable curves $\\overline{\\mathcal{M}}_{g\,n}$\, depending 
 on the choice of a stability condition.\nIn this talk I will begin by intr
 oducing these compactified universal Jacobians\, and explain how their mod
 uli spaces can be constructed using Geometric Invariant Theory (GIT). I wi
 ll then introduce new analogues of these moduli stacks\, where the sheaves
  being parametrised are of a fixed unstable Harder&mdash\;Narasimhan type\
 , and explain how non-reductive GIT allows one to prove the existence of q
 uasi-projective moduli spaces for these stacks\, which in many cases are n
 aturally projective.\n&nbsp\;\nThis talk is based on arXiv:2210.11457 and 
 upcoming work.
LOCATION:Seminar Room 2\, Newton Institute
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