Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Batyrev-Tschinkel conjecture for a non-normal cubic surface and its
  symmetric square   We complete the study of points of bounded height on irreducible non-normal
cubic surfaces by doing the point count on the cubic surface $W$ given by
$t_0^2 t_2 = t_1^2 t_3$ over any number field. We show that the order of growth
agrees with a conjecture by Batyrev and Manin and that the constant reflects
the geometry of the variety as predicted by a conjecture of Batyrev and
Tschinkel. We then provide the point count for its symmetric square
$\mathrm{Sym}^2 W$. Although we can explain the main term of the counting
function, the Batyrev--Manin conjecture is only satisfied after removing a thin
set. Finally we interpret the main term of the count on $\mathrm{Sym}^2(\mathbb
P^2 \times \mathbb P^1)$ done by Le Rudulier using these conjecture.

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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess