### Abstract

Let L be a holomorphic line bundle over a compact Kähler manifold X endowed with a singular Hermitian metric h with curvature current c_{1} (L, h) ≥ 0. In certain cases when the wedge product c_{1} (L,h) ^{κ} is a well defined current for some positive integer κ ≤ dim X, we prove that c_{1} (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 L^{2}-holomorphic sections of the adjoint bundles L^{p} ⊗ 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 c_{1} (L, h)^{κ} using currents of integration over the common zero sets of κ-tuples of sections of L^{p} ⊗ Kx.

Original language | English (US) |
---|---|

Pages (from-to) | 373-386 |

Number of pages | 14 |

Journal | Mathematical Reports |

Volume | 15 |

Issue number | 4 |

State | Published - 2013 |

### Keywords

- Currents
- Kahler manifolds
- Singular hermitian metrics

### ASJC Scopus subject areas

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

## Fingerprint Dive into the research topics of 'On the approximation of positive closed currents on compact Kähler manifolds'. Together they form a unique fingerprint.

## Cite this

*Mathematical Reports*,

*15*(4), 373-386.