曲线奇点与δ不变量的等价性

中文摘要 AI 辅助

我们证明：若代数闭域上的完备既约诺特曲线的两个参数化在极大理想的足够高次幂下同余，则这两个参数化等价，这强化了Greuel和Pfister给出的一些界。此外，我们证明：若两个既约不可约曲线奇点在各自极大理想的足够高且相同的次幂下同构，则这两条曲线的完备化同构，且全完备化的同构在极大理想的某个较低次幂下与原同构一致。我们对该较低次幂给出了新的更优界，强化了Hironaka的界。

英文摘要

We prove that if two parameterizations of a complete reduced noetherian curve over an algebraically closed field agree modulo a sufficiently large power of the maximal ideal, then the two parameterizations are equivalent. This strengthens some bounds from Greuel and Pfister. In addition, we prove that if two reduced and irreducible curve singularities are isomorphic modulo sufficiently high (and identical) powers of their respective maximal ideals, then the completions of the two curves are isomorphic, and the isomorphism of the full completions agrees with the original isomorphism modulo some lower power of the maximal ideals. We provide a new and better bound on the lower power, strengthening the bound in Hironaka

发表机构

• DHBW Mannheim（曼海姆应用科技大学）
• Purdue University（普渡大学）

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