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CATEGORIES:Algebraic Geometry Seminar
SUMMARY:On the K-stability of polarized varieties - Yuji O
daka (Kyoto)
DTSTART;TZID=Europe/London:20110316T141500
DTEND;TZID=Europe/London:20110316T151500
UID:TALK28598AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/28598
DESCRIPTION:The original GIT-stability notion\nfor a polarized
variety is\n"asymptotic (Chow or Hilbert) stabili
ty"\, studied by Mumford and Gieseker\nin the 1970
s\, and some moduli spaces were constructed as con
sequences. Recently a\nversion was introduced with
a differential geometric motivation\, so-called\n
"K-stability"\, by Tian (1997) and reformulated by
Donaldson (2002)\, with the goal of\nestablishing
an equivalence between "stability" and the\nexist
ence of "canonical" metrics. The notion is subtly
different from the\noriginal "asymptotic stability
".\n\nWe give an applicable formula of Donaldson's
Futaki\ninvariants\, which defines K-stability as
(a sort of) "GIT weight"\, after\nDonaldson\, Ros
s-Thomas and X.Wang.\n\nBased on it\, we show that
:\n(1) (K-)semistability implies ``semi-log-canoni
city"\n(partially observed in the 1970s).\n\n(2) T
he converse holds in the canonically polarized cas
e (among others).\n\nThis yields a natural expecta
tion on the construction of Moduli\, which can be\
nseen as an algebraized version of the Fujiki-Dona
ldson picture.
LOCATION:MR13\, CMS
CONTACT:Burt Totaro
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