Monodromy Filtrations and the Topology of Tropical Varieties

Helm, David ; Katz, Eric

Canadian journal of mathematics, Tome 64 (2012) no. 4, pp. 845-868

Résumé

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 ${{\Gamma }_{X}}$ .

Détail

DOI : 10.4153/CJM-2011-067-9

Mots-clés : 14T05, 14D06

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