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Balanced metrics on vector bundles and polarized manifolds
Author(s) -
GarciaFernandez Mario,
Ross Julius
Publication year - 2013
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pds074
Subject(s) - mathematics , vector bundle , pure mathematics , hermitian manifold , metric (unit) , scalar curvature , hermitian matrix , holomorphic function , line bundle , limit (mathematics) , limit of a sequence , manifold (fluid mechanics) , fubini–study metric , curvature , chern class , ample line bundle , mathematical analysis , equivalence of metrics , fisher information metric , product metric , metric space , geometry , mechanical engineering , operations management , engineering , economics
We consider a notion of balanced metrics for triples ( X , L , E ) which depend on a parameter α, where X is a smooth complex manifold with an ample line bundle L and E is a holomorphic vector bundle over X . For generic choice of α, we prove that the limit of a convergent sequence of balanced metrics leads to a Hermitian–Einstein metric on E and a constant scalar curvature Kähler metric in c 1 ( L ). For special values of α, limits of balanced metrics are solutions of a system of coupled equations relating a Hermitian–Einstein metric on E and a Kähler metric in c 1 ( L ).