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CATEGORIES:Algebraic Geometry Seminar
SUMMARY:Igusa quartic and and Wiman-Edge sextics - Ivan Ch
eltsov (Edinburgh)
DTSTART;TZID=Europe/London:20170510T141500
DTEND;TZID=Europe/London:20170510T151500
UID:TALK71181AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/71181
DESCRIPTION:The automorphism group of Igusa quartic is the sym
metric group of degree 6.\nThere are other quartic
threefolds that admit a faithful action of this g
roup.\nOne of them is the famous Burkhardt quartic
threefold.\nTogether they form a pencil that cont
ains all $\\mathfrak{S}_6$-symmetric quartic three
folds.\nArnaud Beauville proved that all but four
of them are irrational\, while Burkhardt and Igusa
quartic are known to be rational.\nCheltsov and S
hramov proved that the remaining two threefolds in
this pencil are also rational.\nIn this talk\, I
will give an alternative prove of both these (irra
tionality and rationality) results.\nTo do this\,
I will describe Q-factorizations of the double cov
er of the four-dimensional projective\nspace branc
hed over the Igusa quartic\, which is known as Cob
le fourfold.\nUsing this\, I will show that $\\mat
hfrak{S}_6$-symmetric quartic threefolds are birat
ional to conic bundles\nover the quintic del Pezzo
surface whose degeneration curves are contained i
n the pencil studied by Wiman and Edge.\nThis is a
joint work with Sasha Kuznetsov and Costya Shramo
v from Moscow.
LOCATION:CMS MR13
CONTACT:Caucher Birkar
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