Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diagonal quartic surfaces with a Brauer-Manin obstruction   In this paper we investigate the quantity of diagonal quartic surfaces $a_0
X_0^4 + a_1 X_1^4 + a_2 X_2^4 +a_3 X_3^4 = 0$ which have a Brauer-Manin
obstruction to the Hasse principle. We are able to find an asymptotic formula
for the quantity of such surfaces ordered by height. The proof uses a
generalization of a method of Heath-Brown on sums over linked variables. We
also show that there exists no uniform formula for a generic generator in this
family.

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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
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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: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn