线丛截面的Skoda划分与伪划分
Skoda division of line bundle sections and pseudo-division
摘要：
本文首先给出了射影簇上线丛的全纯截面的Skoda型除法定理，与以往的定理相比，该定理是最一般的。它是从Varolin定理作为推论导出的。然后，我们重新审视几何有效零点，并观察到，即使是这种一般的斯柯达划分是远远不够的，以产生更强的几何有效零点，如“消失阶$1$划分”，它可以用于有限生成的部分环的基本有限生成引理。为了解决这个问题，我们提出了伪除法的概念，并证明了它可以取代有限生成引理中的通常除法。当线丛充足时，我们也给出了一个消失阶为1的伪除法结果。
英文摘要：
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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