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SUMMARY:The  transcendental motive  of a  a cubic fourfold - Claudio Pedri
 ni (Università degli Studi di Genova)
DTSTART:20200227T111500Z
DTEND:20200227T121500Z
UID:TALK140464@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:&nbsp\;The transcendental part $t(X)$ of the motive of a cubic
  fourfold&nbsp\; $X$&nbsp\; is isomorphic to the (twisted) transcendental 
 part $h^{tr}_2(F(X))$ in a suitable Chow-K\\"unneth decomposition for the 
 motive of the Fano variety of lines $F(X)$. Similarly to the case of a cub
 ic 3-fold\, the transcendental motive $t(X)$ is isomorphic to the {\\it Pr
 ym motive} associated to the surface $S_l \\subset F(X)$ of lines meeting 
 a general line $l$. If $X$ is a special cubic fourfold in the sense of Hod
 ge theory\,&nbsp\; and $F(X) \\simeq S^{[2]}$\, with $S$ a K3 surface then
 &nbsp\; &nbsp\; &nbsp\;$t(X)\\simeq t_2(S)(1)$\, where $t_2(S)$ is the tra
 nscendental motive.&nbsp\; If $X$ is very general then $t(X)$ cannot be is
 omorphic to the (twisted) transcendental motive of a surface.&nbsp\; The e
 xistence&nbsp\; of an isomorphism $t(X) \\simeq t_2(S)(1)$ is related to t
 he&nbsp\; conjectures by Hassett and Kuznetsov on the rationality of a spe
 cial cubic fourfold.&nbsp\; I will also consider the case of&nbsp\; other 
 hyper-K\\"alher varieties than $F(X)$ associated to a cubic fourfold $X$.<
 br><br><br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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