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SUMMARY:Graded linearisations for linear algebraic group actions - Frances
  Kirwan (University of Oxford)
DTSTART:20170818T103000Z
DTEND:20170818T113000Z
UID:TALK76111@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-authors: Gergely Berczi		(ETH Zurich)\, Brent Doran		
 (ETH Zurich)        <br></span><br>In algebraic geometry it is often usefu
 l to be able to construct quotients of algebraic  varieties by linear alge
 braic group actions\; in particular moduli spaces (or stacks)  can be cons
 tructed in this way. When the linear algebraic group is reductive\, and we
  have a suitable linearisation for its action on a projective variety\, we
  can use Mumford&#39\;s geometric invariant theory (GIT) to construct and 
 study such quotient varieties. The aim of this talk is to describe how Mum
 ford&#39\;s GIT can be extended effectively to actions of linear algebraic
  groups which are not necessarily reductive\, with the extra data of a gra
 ded linearisation for the action. Any linearisation in the traditional sen
 se for a reductive group action can be regarded as a graded linearisation 
 in a natural way.  <br><span><br>The classical examples of moduli spaces w
 hich can be constructed using Mumford&#39\;s GIT are the moduli spaces of 
 stable curves and of (semi)stable bundles over a fixed curve. This more ge
 neral construction can be used to construct moduli spaces of unstable obje
 cts\, such as unstable curves (with suitable fixed discrete invariants) or
  unstable bundles (with fixed Harder-Narasimhan type).</span>
LOCATION:Seminar Room 1\, Newton Institute
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