Discriminants and Higher K-energies on Polarized Kähler Manifolds

2015/07/04 by Quinton Westrich, Westrich, Quinton · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1507.01152

15 pages

arxiv created 2015/09/16 · arxiv updated 2015/09/17

Abstract

Given a compact polarized Kähler manifold X\hookrightarrow\mathbbCP^N, the space of Bergman metrics on X, parameterized by SL(N+1,ℂ), corresponds to a dense set in the space of Kähler potentials in the Kähler class as N→∞. Critical points of the kth K-energy functional, which is defined on the Kähler class, correspond to metrics with harmonic kth Chern form. In this paper it is shown that the higher K-energy functionals, when restricted to the Bergman metrics, are expressible as the energies of certain pairs of vectors (tensors products of discriminants). Consequentially, we obtain results on the asymptotic behavior of these functionals along 1-parameter subgroups and their boundedness properties.

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