Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Jacobians among Abelian threefolds: a formula of Klein and a question of
  Serre   Let k be a field and f be a Siegel modular form of weight h \geq 0 and genus
g>1 over k. Using f, we define an invariant of the k-isomorphism class of a
principally polarized abelian variety (A,a)/k of dimension g. Moreover when
(A,a) is the Jacobian of a smooth plane curve, we show how to associate to f a
classical plane invariant. As straightforward consequences of these
constructions, when g=3 and k is a subfield of the complex field, we obtain (i)
a new proof of a formula of Klein linking the modular form \chi_{18} to the
square of the discriminant of plane quartics ; (ii) a proof that one can decide
when (A,a) is a Jacobian over k by looking whether the value of \chi_{18} at
(A,a) is a square in k. This answers a question of J.-P. Serre. Finally, we
study the possible generalizations of this approach for g>3.

24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat