Skoda division of line bundle sections and pseudo-division

Dano Kim

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arXiv · 1408.6569

Skoda division of line bundle sections and pseudo-division

Dano Kim

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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 $1$ 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.

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BibTeX RIS

Dano Kim. 2014-08-27. Skoda division of line bundle sections and pseudo-division. https://arxiv.org/abs/1408.6569

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