Balanced metrics on vector bundles and polarized manifolds | Zendy

GarciaFernandez Mario | Zendy; Ross Julius | Zendy

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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 ).

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