关于全纯函数芽对的米尔诺数和蒂尤林数
On Milnor and Tjurina numbers of Pairs of Holomorphic Functions Germs
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中文总结 AI 辅助
该研究受全纯函数芽对的米尔诺数分岔公式启发，通过叶状理论引入蒂尤林数，证明其为解析不变量并推导公式及性质，还用此不变量刻画半驯亚纯函数芽，同时研究了全纯函数芽对的米尔诺数相关性质。
中文摘要 AI 辅助
受全纯函数芽对的米尔诺数的分岔公式启发，我们通过叶状理论引入此类对的蒂尤林数。我们证明它是一个解析不变量，推导其显式公式并建立其若干性质，包括分岔公式。作为应用，我们用此不变量刻画半驯亚纯函数芽。我们还研究了全纯函数芽对的米尔诺数的若干性质，特别为对建立了泰西耶引理的一个版本，推导了对的米尔诺数的一个上界，并将这些结果应用于代数曲线的一般铅笔。
英文摘要
Motivated by the bifurcation formula for the Milnor number of pairs of holomorphic function germs, we introduce, via foliation theory, the Tjurina number of such pairs. We prove that this is an analytic invariant, derive an explicit formula for it, and establish several of its properties, including a bifurcation formula. As an application, we characterize semitame meromorphic function germs in terms of this invariant. We also investigate several properties of the Milnor number of a pair of holomorphic function germs. In particular, we establish a version of Teissier's Lemma for pairs, derive an upper bound for the Milnor number of a pair, and apply these results to generic pencils of algebraic curves.
