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UID:news779@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20190212T181018
DTSTART;TZID=Europe/Zurich:20110513T000000
SUMMARY:Seminar Algebra and Geometry: Ivan Arzhantsev (Moscow State Univers
 ity and Institut Fourier)
DESCRIPTION:(joint work with Devrim Celik and Juergen Hausen)We begin with 
 a survey of known results concerning categorical quotients.Given  an actio
 n of an affine algebraic group with only trivial characters on a  factoria
 l variety\, we characterize existence of categorical quotient in  the cate
 gory of algebraic varieties. Moreover\, allowing  constructible sets as qu
 otients\, we obtain a more general existence  result\, which\, for example
 \, settles the case of a finitely generated  algebra of invariants. As an 
 application\, we provide a combinatorial  GIT-type construction of categor
 ial quotients for actions on\, e.g.  complete\, varieties with finitely ge
 nerated Cox ring via lifting to the  universal torsor.
X-ALT-DESC: (joint work with Devrim Celik and Juergen Hausen)<br /><br />We
  begin with a survey of known results concerning categorical quotients.<br
  />Given  an action of an affine algebraic group with only trivial charact
 ers on a  factorial variety\, we characterize existence of categorical quo
 tient in  the category of algebraic varieties. Moreover\, allowing  constr
 uctible sets as quotients\, we obtain a more general existence  result\, w
 hich\, for example\, settles the case of a finitely generated  algebra of 
 invariants. As an application\, we provide a combinatorial  GIT-type const
 ruction of categorial quotients for actions on\, e.g.  complete\, varietie
 s with finitely generated Cox ring via lifting to the  universal torsor.
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