论文标题
超平面部分的最小指数：Teissier的猜想
Minimal exponents of hyperplane sections: a conjecture of Teissier
论文作者
论文摘要
我们证明了Teissier的猜想，说明如果$ f $在$ p $和$ h $中具有孤立的奇异性，而$ h $是$ p $的平稳性超出表面，则是$ \widetildeα_p（f）\ geq \ geq \ geq \widetildealeα_p（f \ vert_h） $\widetildeα_P(f)$ and $\widetildeα_P(f\vert_H)$ are the minimal exponents at $P$ of $f$ and $f\vert_H$, respectively, and $θ_P(f)$ is an invariant obtained by comparing the integral closures of the powers of the Jacobian ideal of $f$ and of the ideal defining $P$.证明是基于Loeser和Elduque-Mustata的方法。新成分是关于霍奇理想在有限图中的行为的结果，以及针对具有恒定米尔诺数的孤立奇异家庭的某些霍奇理想的行为的结果。在相反的方向上，我们表明，对于每$ f $，如果$ h $是$ p $的一般性高度，则是$ \widetildeα_p（f）\ leq \ leq \ leq \widetildeα_p（f \ vert_h）+\ frac {1} {1} {{{\ rm mult} _p（f rm mult} _p（f）_p（f）_p（f）n exterial case nirection a nirection，lo sriped a sriperieling case nistor。
We prove a conjecture of Teissier asserting that if $f$ has an isolated singularity at $P$ and $H$ is a smooth hypersurface through $P$, then $\widetildeα_P(f)\geq \widetildeα_P(f\vert_H)+\frac{1}{θ_P(f)+1}$, where $\widetildeα_P(f)$ and $\widetildeα_P(f\vert_H)$ are the minimal exponents at $P$ of $f$ and $f\vert_H$, respectively, and $θ_P(f)$ is an invariant obtained by comparing the integral closures of the powers of the Jacobian ideal of $f$ and of the ideal defining $P$. The proof builds on the approaches of Loeser and Elduque-Mustata. The new ingredients are a result concerning the behavior of Hodge ideals with respect to finite maps and a result about the behavior of certain Hodge ideals for families of isolated singularities with constant Milnor number. In the opposite direction, we show that for every $f$, if $H$ is a general hypersurface through $P$, then $\widetildeα_P(f)\leq \widetildeα_P(f\vert_H)+\frac{1}{{\rm mult}_P(f)}$, extending a result of Loeser from the case of isolated singularities.
