Skoda division of line bundle sections and pseudo-division
Abstract
We first present a Skoda type division theorem for holomorphic sections of line bundles on a projective variety which is essentially the most general, compared to previous ones. It is derived from Varolin's theorem as a corollary. Then we revisit Geometric Effective Nullstellensatz and observe that even this general Skoda division is far from sufficient to yield stronger Geometric Effective Nullstellensatz such as `vanishing order division', which could be used for finite generation of section rings by the basic finite generation lemma. To resolve this problem, we develop a notion of pseudo-division and show that it can replace the usual division in the finite generation lemma. We also give a vanishing order 1 pseudo-division result when the line bundle is ample.
Keywords
Cite
@article{arxiv.1408.6569,
title = {Skoda division of line bundle sections and pseudo-division},
author = {Dano Kim},
journal= {arXiv preprint arXiv:1408.6569},
year = {2014}
}