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SUMMARY:The weighted Hermite--Einstein equation - Michael Hallam (Aarhus U
 niversitet)
DTSTART:20240509T100000Z
DTEND:20240509T110000Z
UID:TALK216733@talks.cam.ac.uk
DESCRIPTION:In joint work with Abdellah Lahdili\, we introduce a new weigh
 ted generalisation of the Hermite--Einstein equation for torus equivariant
  vector bundles over compact K&auml\;hler manifolds. The novel equation re
 covers various canonical Hermitian metrics on vector bundles in interestin
 g geometric situations---examples include K&auml\;hler--Ricci solitons\, a
 s well as the transverse Hermite--Einstein metrics on Sasaki manifolds stu
 died by Biswas--Schumacher and Baraglia--Hekmati. Extending the equivarian
 t intersection theory introduced by Inoue to arbitrary weight functions on
  the moment polytope\, we define the weighted slope of a vector bundle\, e
 xtend the Kobayashi--L&uuml\;bke inequality to the weighted setting\, and 
 give a proof of the moment map property of the weighted Hermite--Einstein 
 equation via fibre integration of equivariant forms\, following the approa
 ch of Dervan--Hallam. As a main result\, we prove the weighted Kobayashi--
 Hitchin correspondence\, namely that a T-equivariant vector bundle admits 
 a weighted Hermite--Einstein metric if and only if the vector bundle is we
 ighted slope polystable.
LOCATION:Seminar Room 1\, Newton Institute
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