Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyperplane arrangements and mixed Hodge numbers of the Milnor fiber   For each complex central essential hyperplane arrangement $\mathcal{A}$, let
$F_{\mathcal{A}}$ denote its Milnor fiber. We use Tevelev's theory of tropical
compactifications to study invariants related to the mixed Hodge structure on
the cohomology of $F_{\mathcal{A}}$. We prove that the map taking each
arrangement $\mathcal{A}$ to the Hodge-Deligne polynomial of $F_{\mathcal{A}}$
is locally constant on the realization space of any loop-free matroid. When
$\mathcal{A}$ consists of distinct hyperplanes, we also give a combinatorial
description for the homotopy type of the boundary complex of any simple normal
crossing compactification of $F_{\mathcal{A}}$. As a direct consequence, we
obtain a combinatorial formula for the top weight cohomology of
$F_{\mathcal{A}}$, recovering a result of Dimca and Lehrer.

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The categories of this paper are: hep-ph
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
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The categories of this paper are: cs
31
The categories of this paper are: ao-sci