Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arakelov-Milnor inequalities and maximal variations of Hodge structure   In this paper we study the $\mathbb{C}^*$-fixed points in moduli spaces of
Higgs bundles over a compact Riemann surface for a complex semisimple Lie group
and its real forms. These fixed points are called Hodge bundles and correspond
to complex variations of Hodge structure. We introduce a topological invariant
for Hodge bundles that generalizes the Toledo invariant appearing for Hermitian
Lie groups. A main result of this paper is a bound on this invariant which
generalizes both the Milnor-Wood inequality of the Hermitian case and the
Arakelov inequalities of classical variations of Hodge structure. When the
generalized Toledo invariant is maximal, we establish rigidity results for the
associated variations of Hodge structure which generalize known rigidity
results for maximal Higgs bundles and their associated maximal representations
in the Hermitian case.

3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ