Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On fibrations approaching the Arakelov equality   The sum of Lyapunov exponents $L_f$ of a semi-stable fibration is the ratio
of the degree of the Hodge bundle by the Euler characteristic of the base. This
ratio is bounded from above by the Arakelov inequality. Sheng-Li Tan showed
that for fiber genus $g\geq 2$ the Arakelov equality is never attained. We
investigate whether there are sequences of fibrations approaching
asymptotically the Arakelov bound. The answer turns out to be no, if the
fibration is smooth, or non-hyperelliptic, or has a small base genus.
  Moreover, we construct examples of semi-stable fibrations showing that
Teichm\"uller curves are not attaining the maximal possible value of $L_f$.

15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol