Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A universal Torelli theorem for elliptic surfaces   Given two semistable, non potentially isotrivial elliptic surfaces over a
curve $C$ defined over a field of characteristic zero or finitely generated
over its prime field, we show that any compatible family of effective
isometries of the N{\'e}ron-Severi lattices of the base changed elliptic
surfaces for all finite separable maps $B\to C$ arises from an isomorphism of
the elliptic surfaces. Without the effectivity hypothesis, we show that the two
elliptic surfaces are isomorphic.
  We also determine the group of universal automorphisms of a semistable
elliptic surface. In particular, this includes showing that the
Picard-Lefschetz transformations corresponding to an irreducible component of a
singular fibre, can be extended as universal isometries. In the process, we get
a family of homomorphisms of the affine Weyl group associated to
$\tilde{A}_{n-1}$ to that of $\tilde{A}_{dn-1}$, indexed by natural numbers
$d$, which are closed under composition.

11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph