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SUMMARY:Jack Rogers (University of Manchester)
DTSTART:20210513T140000Z
DTEND:20210513T150000Z
DTSTAMP:20260423T035958Z
UID:ZAG/120
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ZAG/120/">K-
 stability of smooth Fano SL2-threefolds</a>\nby Jack Rogers (University of
  Manchester) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstrac
 t\nThere has been much interest in K-stability since it was shown to be eq
 uivalent to the existence of Kähler-Einstein metrics by Chen-Donaldson-Su
 n. The theory of K-stability is now well developed\, but practical methods
  to check whether a given variety is K-stable are hard to come by. Equivar
 iant K-stability\, introduced by Datar-Székelyhidi\, makes finding such c
 riteria easier for varieties with large automorphism groups.\n\nIf an alge
 braic group G acts on a variety X\, the complexity of the action is the mi
 nimal codimension in X of the orbits of a Borel subgroup B of G (e.g. if T
  is a torus\, the complexity zero T-varieties are the toric varieties). Co
 nditions for K-stability have been found for toric varieties by Wang-Zhu\,
  for complexity one T-varieties by Ilten-Süss and for all complexity zero
  varieties by Delcroix.\n\nWe will discuss the combinatorial description d
 ue to Timashev of complexity one G-varieties\, and describe a practical me
 thod to check K-stability in the particular case of smooth Fano SL2-threef
 olds. In particular\, this method proves the K-stability of several variet
 ies not previously known to be K-stable\, e.g. projective 3-space blown up
  along three disjoint lines. This is joint work with Hendrik Süss.\n
LOCATION:https://researchseminars.org/talk/ZAG/120/
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