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arXiv · 1711.02045

Convexity of complements of tropical varieties, and approximations of currents

Karim Adiprasito·Farhad Babaee
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Abstract

The goal of this note is to affirm a local version of the conjecture of Nisse--Sottile [NS16] on higher convexity of complements of tropical varieties, while providing a family of counter-examples for the global Nisse--Sottle conjecture in any codimension and dimension higher than 1. Moreover, it will be shown that, surprisingly, this family also provides a family of counter-examples for the generalized Hodge conjecture for positive currents in these dimensions, and gives rise to further approximability obstruction.

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Karim Adiprasito, Farhad Babaee. 2017-11-06. Convexity of complements of tropical varieties, and approximations of currents. https://doi.org/10.1007/s00208-018-1728-2

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