Convexity of complements of tropical varieties, and approximations of currents

Karim Adiprasito*, Farhad Babaee

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 languageAmerican English
Pages (from-to)237-251
Number of pages15
JournalMathematische Annalen
Volume373
Issue number1-2
DOIs
StatePublished - 8 Feb 2019

Bibliographical note

Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

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