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SUMMARY:Coupled Equations\, cscK metrics and geodesic stability - Garcia-F
 ernandez\, M (Aarhus Universitet)
DTSTART:20110127T140000Z
DTEND:20110127T150000Z
UID:TALK29659@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We introduce a system of partial differential equations coupli
 ng a Khler metric on a compact complex manifold X and a connection on a pr
 incipal bundle over X. These equations generalize the constant scalar curv
 ature equation for a Khler metric on a complex manifold and the Hermitian-
 Yang-Mills equations for a connection on a bundle. They have an interpreta
 tion in terms of a moment map\, where the group of symmetries is an extens
 ion of the gauge group of the bundle that moves the base X. We develop a n
 atural "formal picture" for the problem which leads to analytic obstructio
 ns for the existence of solutions. When the structure group of the bundle 
 is trivial we recover known obstructions for the theory of cscK metrics\, 
 in particular the Futaki invariant and the notion of geodesic stability. T
 his is joint work with Luis Alvarez Consul and Oscar Garcia Prada.\n
LOCATION:Seminar Room 1\, Newton Institute
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