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SUMMARY:Igusa quartic and and Wiman-Edge sextics - Ivan Cheltsov (Edinburg
 h)
DTSTART:20170510T131500Z
DTEND:20170510T141500Z
UID:TALK71181@talks.cam.ac.uk
CONTACT:Caucher Birkar
DESCRIPTION:The automorphism group of Igusa quartic is the symmetric group
  of degree 6.\nThere are other quartic threefolds that admit a faithful ac
 tion of this group.\nOne of them is the famous Burkhardt quartic threefold
 .\nTogether they form a pencil that contains all $\\mathfrak{S}_6$-symmetr
 ic quartic threefolds.\nArnaud Beauville proved that all but four of them 
 are irrational\, while Burkhardt and Igusa quartic are known to be rationa
 l.\nCheltsov and Shramov proved that the remaining two threefolds in this 
 pencil are also rational.\nIn this talk\, I will give an alternative prove
  of both these (irrationality and rationality) results.\nTo do this\, I wi
 ll describe Q-factorizations of the double cover of the four-dimensional p
 rojective\nspace branched over the Igusa quartic\, which is known as Coble
  fourfold.\nUsing this\, I will show that $\\mathfrak{S}_6$-symmetric quar
 tic threefolds are birational to conic bundles\nover the quintic del Pezzo
  surface whose degeneration curves are contained in the pencil studied by 
 Wiman and Edge.\nThis is a joint work with Sasha Kuznetsov and Costya Shra
 mov from Moscow.
LOCATION:CMS MR13
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