On the approximation of positive closed currents on compact Kähler manifolds

Dan Coman, George Marinescu

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

Let L be a holomorphic line bundle over a compact Kähler manifold X endowed with a singular Hermitian metric h with curvature current c1 (L, h) ≥ 0. In certain cases when the wedge product c1 (L,h) κ is a well defined current for some positive integer κ ≤ dim X, we prove that c1 (L,h)κ can be approximated by averages of currents of integration over the common zero sets of κ-tuples of holomorphic sections over X of the high powers L p:= L⊗p. In the second part of the paper, we study the convergence of the Fubini-Study currents and the equidistribution of zeros of L2-holomorphic sections of the adjoint bundles Lp ⊗ Kx, where L is a holomorphic line bundle over a complex manifold X endowed with a singular Hermitian metric h with positive curvature current. As an application, we obtain an approximation theorem for the current c1 (L, h)κ using currents of integration over the common zero sets of κ-tuples of sections of Lp ⊗ Kx.

Original languageEnglish (US)
Pages (from-to)373-386
Number of pages14
JournalMathematical Reports
Volume15
Issue number4
StatePublished - 2013

Keywords

  • Currents
  • Kahler manifolds
  • Singular hermitian metrics

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology
  • Applied Mathematics

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