Convexity of complements of tropical varieties, and approximations of currents

Karim Adiprasito, Farhad Babaee

Research output: Contribution to journalArticle (Academic Journal)peer-review

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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.
Original languageEnglish
Number of pages15
JournalMathematische Annalen
Early online date16 Jul 2018
DOIs
Publication statusE-pub ahead of print - 16 Jul 2018

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