Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal exponents of hyperplane sections: a conjecture of Teissier   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
$\widetilde{\alpha}_P(f)\geq
\widetilde{\alpha}_P(f\vert_H)+\frac{1}{\theta_P(f)+1}$, where
$\widetilde{\alpha}_P(f)$ and $\widetilde{\alpha}_P(f\vert_H)$ are the minimal
exponents at $P$ of $f$ and $f\vert_H$, respectively, and $\theta_P(f)$ 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
$\widetilde{\alpha}_P(f)\leq \widetilde{\alpha}_P(f\vert_H)+\frac{1}{{\rm
mult}_P(f)}$, extending a result of Loeser from the case of isolated
singularities.

23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph