Monodromy Filtrations and the Topology of Tropical Varieties
Monodromy Filtrations and the Topology of Tropical Varieties
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单峰过滤和热带品种的拓扑结构
DOI：
10.4153/cjm-2011-067-9
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Eric Katz
中科院分区：
文献类型：
--
作者：
David Helm;Eric Katz
Abstract 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 ${{\Gamma }_{X}}$ .
Abstract 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 ${{\Gamma }_{X}}$ .