Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Families of K3 surfaces over curves satisfying the equality of
  Arakelov-Yau's type and modularity   Let $f:X\to C$ be a family of semistable K3 surfaces with non-empty set $S$
of singular fibres having infinite local monodromy. Then, when the so called
Arakelov-Yau inequality reaches equality, we prove that $C\setminus S$ is a
modular curve and the family comes essentially from a family of elliptic curves
through a so called Nikulin-Kummer construction. In particular, when $C=\BBb
P^1$, the family of elliptic curves must be one of Beauville's 6 examples where
Arakelov inequality reaches equality.

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The categories of this paper are: comp-gas
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom