Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convexity of complements of tropical varieties, and approximations of
  currents   The goal of this note is to affirm a local version of the conjecture of
Nisse--Sottile [NS16] on higher convexity of complements of tropical varieties,
while providing a family of counter-examples for the global Nisse--Sottle
conjecture in any codimension and dimension higher than 1. Moreover, it will be
shown that, surprisingly, this family also provides a family of
counter-examples for the generalized Hodge conjecture for positive currents in
these dimensions, and gives rise to further approximability obstruction.

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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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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: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org