Geometric properties of upper level sets of Lelong numbers on projective spaces

Dan Coman; Tuyen Trung Truong

Geometric properties of upper level sets of Lelong numbers on projective spaces

Complex Variables 2013-05-07 v1 Algebraic Geometry

Authors: Dan Coman , Tuyen Trung Truong

Abstract

Let $T$ be a positive closed current of unit mass on the complex projective space $\mathbb P^n$ . For certain values $\alpha<1$ , we prove geometric properties of the set of points in $\mathbb P^n$ where the Lelong number of $T$ exceeds $\alpha$ . We also consider the case of positive closed currents of bidimension (1,1) on multiprojective spaces.

Keywords

Lelong numbers positive closed currents projective spaces upper level sets complex geometry bidimension (1,1) multiprojective spaces

Cite

@article{arxiv.1305.0864,
  title  = {Geometric properties of upper level sets of Lelong numbers on projective spaces},
  author = {Dan Coman and Tuyen Trung Truong},
  journal= {arXiv preprint arXiv:1305.0864},
  year   = {2013}
}

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