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DTSTART:20180325T030000
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DTSTART:20181028T020000
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DTSTAMP:20210617T073513Z
UID:59cb91e567fb9385976902@ist.ac.at
DTSTART:20181004T133000
DTEND:20181004T153000
DESCRIPTION:Speaker: Patakfalvi Zsolt\nhosted by Tamas Hausel\nAbstract: Th
e Chow-Mumford (CM) line bundle is a functorial line bundle on the base of
any family of polarized varieties\, in particular on the base of families
of Q-Fano varieties (that is\, Fano varieties with klt singularities). It
is conjectured that it yields a polarization on the conjectured moduli sp
ace of K-semi-stable Q-Fano varieties. This boils down to showing semi-pos
itivity/positivity statements about the CM-line bundle for families with
$K$-semi-stable/$K$-polystable Q-Fano fibers. I present a joint work with
Giulio Codogni where we prove the necessary semi-positivity statements in
the $K$-semi-stable situation\, and the necessary positivity statements in
the uniform $K$-stable situation\, including in both cases variants assu
ming $K$-stability only for very general fibers. Our statements work in t
he most general singular situation (klt singularities)\, and the proofs ar
e algebraic\, except the computation of the limit of a sequence of real nu
mbers via the central limit theorem of probability theory. I also present
a birational geometry application to the classification of Fano varieties
LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS
T Austria
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Positivity of the Chow-Mumford line bundle for families of K-stable
Q-Fano varieties
URL:https://talks-calendar.app.ist.ac.at/events/1463
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