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SUMMARY:On the K-stability of polarized varieties - Yuji Odaka (Kyoto)
DTSTART:20110316T141500Z
DTEND:20110316T151500Z
UID:TALK28598@talks.cam.ac.uk
CONTACT:Burt Totaro
DESCRIPTION:The original GIT-stability notion\nfor a polarized variety is\
 n"asymptotic (Chow or Hilbert) stability"\, studied by Mumford and Gieseke
 r\nin the 1970s\, and some moduli spaces were constructed as consequences.
  Recently a\nversion was introduced with a differential geometric motivati
 on\, so-called\n"K-stability"\, by Tian (1997) and reformulated by Donalds
 on (2002)\, with the goal of\nestablishing an equivalence between "stabili
 ty" and the\nexistence of "canonical" metrics. The notion is subtly differ
 ent from the\noriginal "asymptotic stability".\n\nWe give an applicable fo
 rmula of Donaldson's Futaki\ninvariants\, which defines K-stability as (a 
 sort of) "GIT weight"\, after\nDonaldson\, Ross-Thomas and X.Wang.\n\nBase
 d on it\, we show that:\n(1) (K-)semistability implies ``semi-log-canonici
 ty"\n(partially observed in the 1970s).\n\n(2) The converse holds in the c
 anonically polarized case (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-Donaldson picture.
LOCATION:MR13\, CMS
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