Monodromy Filtrations and the Topology of Tropical Varieties
Canadian journal of mathematics, Tome 64 (2012) no. 4, pp. 845-868
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We study the topology of tropical varieties that arise from a certain natural class of varieties. We use the theory of tropical degenerations to construct a natural, “multiplicity-free” parameterization of Trop $\left( X \right)$ by a topological space ${{\Gamma }_{X}}$ and 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 $X$ which constrain the topology of Trop $\left( X \right)$ . We also obtain a description of the top power of the monodromy operator acting on middle cohomology of $X$ in terms of the volume pairing on ${{\Gamma }_{X}}$ .
Helm, David; Katz, Eric. Monodromy Filtrations and the Topology of Tropical Varieties. Canadian journal of mathematics, Tome 64 (2012) no. 4, pp. 845-868. doi: 10.4153/CJM-2011-067-9
@article{10_4153_CJM_2011_067_9,
author = {Helm, David and Katz, Eric},
title = {Monodromy {Filtrations} and the {Topology} of {Tropical} {Varieties}},
journal = {Canadian journal of mathematics},
pages = {845--868},
year = {2012},
volume = {64},
number = {4},
doi = {10.4153/CJM-2011-067-9},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-067-9/}
}
TY - JOUR AU - Helm, David AU - Katz, Eric TI - Monodromy Filtrations and the Topology of Tropical Varieties JO - Canadian journal of mathematics PY - 2012 SP - 845 EP - 868 VL - 64 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-067-9/ DO - 10.4153/CJM-2011-067-9 ID - 10_4153_CJM_2011_067_9 ER -
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