Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Classification of Elliptic Fibrations modulo Isomorphism on K3
  Surfaces with large Picard Number   Motivated by a problem originating in string theory, we study elliptic
fibrations on K3 surfaces with large Picard number modulo isomorphism. We give
methods to determine upper bounds for the number of inequivalent K3 surfaces
sharing the same frame lattice. For any given Neron--Severi lattice $S_X$, such
a bound on the `multiplicity' can be derived by investigating the quotient of
the isometry group of $S_X$ by the automorphism group. The resulting bounds are
strongest for large Picard numbers and multiplicities of unity do indeed occur
for a number of K3 surfaces with Picard number 20. Under a few extra
conditions, a more refined analysis is also possible by explicitly studying the
embedding of $S_X$ into the even unimodular lattice ${\rm II}_{1,25}$ and
exploiting the detailed structure of the isometry groups of $S_X$ and ${\rm
II}_{1,25}$. We illustrate these methods in examples and derive bounds for the
number of elliptic fibrations on Kummer surfaces of Picard numbers 17 and 20.
As an intermediate step, we also discuss coarser classification schemes and
review known results.

4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc