Higher Connectivity of Tropicalizations
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Abstract
We show that the tropicalization of an irreducible d-dimensional variety over a field of characteristic 0is (d-l)-connected through codimension one, where l is the dimension of the lineality space of the tropicalization. From this we obtain a higher connectivity result for skeleta of rational polytopes. We also prove a tropical analogue of the Bertini Theorem: the intersection of the tropicalization of an irreducible variety with a generic hyperplane is again the tropicalization of an irreducible variety.Keywords
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This publication has 15 references indexed in Scilit:
- Algebraic matroids and set-theoretic realizability of tropical varietiesJournal of Combinatorial Theory, Series A, 2017
- On fewnomials, integral points, and a toric version of Bertini’s theoremJournal of the American Mathematical Society, 2017
- Do most polynomials generate a prime ideal?Journal of Algebra, 2016
- Stable intersections of tropical varietiesJournal of Algebraic Combinatorics, 2015
- Local Tropical Linear SpacesDiscrete & Computational Geometry, 2013
- On the Graph Connectivity of Skeleta of Convex PolytopesDiscrete & Computational Geometry, 2009
- Fibers of tropicalizationMathematische Zeitschrift, 2008
- Computing tropical varietiesJournal of Symbolic Computation, 2007
- The Bergman complex of a matroid and phylogenetic treesJournal of Combinatorial Theory, Series B, 2006
- Incidence graphs of convex polytopesJournal of Combinatorial Theory, 1967