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SUMMARY:Stability of pairs and Kähler geometry - Ruadhaí Dervan\, Univer
 sity of Glasgow
DTSTART:20241023T131500Z
DTEND:20241023T141500Z
UID:TALK221680@talks.cam.ac.uk
CONTACT:Dhruv Ranganathan
DESCRIPTION:Geometric invariant theory (GIT) is the quotient theory of alg
 ebraic geometry\, which applies to group actions on varieties together wit
 h an ample line bundle. The main point of GIT is that only the "stable" or
 bits are parametrised in the quotient. \n\nIn applications\, the ampleness
  hypothesis frequently fails\, or is at least not known to hold. I will de
 scribe a generalisation of some of the ideas of GIT to more general line b
 undles\, where one writes the given line bundle as the difference of a pai
 r of ample line bundles. The most interesting aspect is that the tradition
 al numerical characterisation of stability is known to be false in this ge
 neral setting\, so to give a numerical characterisation\, some new geometr
 ic input is needed.\n\nI will then describe some applications to Kähler g
 eometry\, such as a new proof that a version of K-stability of a smooth Fa
 no variety is equivalent to the existence of a Kähler-Einstein metric. \n
 \nThis is all joint work with Rémi Reboulet.
LOCATION:CMS MR13
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