Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monodromy Filtrations and the Topology of Tropical Varieties   We find restrictions on the topology of tropical varieties that arise from a
certain natural class of varieties. We develop a theory of tropical
degenerations that is a nonconstant coefficient analogue of Tevelev's theory of
tropical compactifications, and use it to construct normal crossings
degenerations of a subvariety X of a torus, under mild hypotheses on X. These
degenerations allow us to construct a natural, "multiplicity-free"
parameterization of Trop(X) by a topological space \Gamma_X. We give a
geometric interpretation of the cohomology of \Gamma_X in terms of the action
of a monodromy operator on the cohomology of X. This gives bounds on the Betti
numbers of $\Gamma_X$ in terms of the Betti numbers of $X$. When $X$ is a
sufficiently general complete intersection, this allows us to show that the
cohomology of Trop(X) vanishes in degree less than dim(X). In addition, we give
a description for the top power of the monodromy operator acting on middle
cohomology in terms of the volume pairing on $\Gamma_X$.

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The categories of this paper are: nlin
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The categories of this paper are: cs
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph