On Zariski Decomposition with and without support
Algebraic Geometry
2013-08-06 v2
Abstract
In this paper we study Zariski Decomposition with support in a negative definite cycle, a variation introduced by Y. Miyaoka. We provide two extensions of the original statement, which was originally meant for effective -divisors: we can either state it for any -divisor, or we can take the support to be in any cycle. Ultimately, we present a new approach to Zariski Decomposition of pseudo-effective -divisors, which consists in iterating Zariski Decomposition with support.
Cite
@article{arxiv.1306.4697,
title = {On Zariski Decomposition with and without support},
author = {Roberto Laface},
journal= {arXiv preprint arXiv:1306.4697},
year = {2013}
}
Comments
14 pages, a second improvement to Miyaoka's original result is added, along with a counterexample which shows that the two extensions are mutually exclusive; minor changes in the text structure, but the other results in the original posting of this paper remain unchanged