Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arithmetics and combinatorics of tropical Severi varieties of univariate
  polynomials   We give a description of the tropical variety of univariate polynomials of
degree n having two double roots. As a set, it is given as the union of three
types of maximal cones of dimension n-1, where only cones of two of these types
are cones of the secondary fan of {0,...,n}. Through Kapranov's theorem, this
goal is achieved by a careful study of the possible valuations of the
elementary symmetric functions of the roots of a polynomial with two double
root. Despite its apparent simplicity, the computation of the tropical Severi
variety has both combinatorial and arithmetic ingredients.

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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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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: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an