Convexity of complements of tropical varieties, and approximations of currents

Karim Adiprasito, Farhad Babaee

Research output: Contribution to journalArticlepeer-review

Abstract

The goal of this note is to affirm a local version of conjecture of Nisse–Sottile [19] 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 one. Moreover, it is 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
Pages (from-to)237-251
Number of pages15
JournalMathematische Annalen
Volume373
Issue number1-2
DOIs
StatePublished - 8 Feb 2019

All Science Journal Classification (ASJC) codes

  • General Mathematics

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