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SUMMARY:Kobayashi-Hitchin correspondence for polarized fibrations [MPIM]
DTSTART:20250220T140000Z
DTEND:20250220T150000Z
DTSTAMP:20260815T092900Z
UID:indico-event-253@math-events.uni-bonn.de
DESCRIPTION:Speakers: Finski Siarhei (Ecole Polytechnique\, Palaiseau/MPIM
 )\n\nMPI-Oberseminar\nA Hermitian metric on a holomorphic vector bundle is
  said to be Hermite-Einstein if its mean curvature is proportional to the 
 identity operator. The Kobayashi-Hitchin correspondence (or the Donaldson-
 Uhlenbeck-Yau theorem) asserts that a holomorphic vector bundle admits a H
 ermite-Einstein metric if and only if it satisfies the algebraic condition
  of slope polystability.\nIn this talk\, I will describe a recent extensio
 n of the Kobayashi-Hitchin correspondence to general fibrations beyond hol
 omorphic vector bundles. Specifically\, for a polarized family of complex 
 projective manifolds\, we examine the so-called Wess-Zumino-Witten (WZW) e
 quation\, which specializes to the Hermite-Einstein equation\, when the po
 larized fibration is associated with a projectivization of a holomorphic v
 ector bundle. We establish that the existence of approximate solutions to 
 this equation is equivalent to the asymptotic semistability of the direct 
 image sheaves associated with high tensor powers of the polarizing line bu
 ndle. We also discuss a relation between this result and the conjecture of
  Demailly concerning the optimality of Holomorphic Morse Inequalities. \n
  \n\nhttps://math-events.uni-bonn.de/event/253/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/253/
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