Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enumeration of Complex and Real Surfaces via Tropical Geometry   We prove a correspondence theorem for singular tropical surfaces in real
three space, which recovers singular algebraic surfaces in an appropriate toric
three-fold that tropicalize to a given singular tropical surface. Furthermore,
we develop a three-dimensional version of Mikhalkin's lattice path algorithm
that enumerates singular tropical surfaces passing through an appropriate
configuration of points in real three space. As application we show that there
are pencils of real surfaces of degree $d$ in projective three space containing
at least $(3/2)d^3+O(d^2)$ singular surfaces, which is asymptotically
comparable to the number $4(d-1)^3$ of all complex singular surfaces in the
pencil. Our result relies on the classification of singular tropical surfaces
(arXiv:1106.2676).

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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th