Abstract

In this paper we prove the Noether theorem with the multiplicities described by PD operators. Despite the known analog versions in this case the provided conditions are necessary and sufficient. We also prove the Cayley–Bacharach theorem with PD multiplicities. As far as we know this is the first generalization of this theorem for multiple intersections.

中文翻译：

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关于PD多重性的Noether和Cayley-Bacharach定理

摘要

在本文中，我们用PD算子描述的多重性证明了Noether定理。尽管在这种情况下是已知的模拟版本，但提供的条件是必要和充分的。我们还证明了PD多重性的Cayley-Bacharach定理。据我们所知，这是该定理对多个交点的首次推广。