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Balanced metrics for vector bundles and polarised manifolds

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    Submitted manuscript, 335 KB, PDF document


  • Mario Garcia Fernandez, Denmark
  • Julius Ross, Cambridge University, United Kingdom
We consider a notion of balanced metrics for triples (X, L, E) which depend on a parameter α, where X is 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 c1(L). For this, we compute the top two terms of the density of states expansion of the Bergman kernel of E ⊗ L^k
Original languageEnglish
Publication statusPublished - 2012

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