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 language | English |
---|---|
Pages (from-to) | 237-251 |
Number of pages | 15 |
Journal | Mathematische Annalen |
Volume | 373 |
Issue number | 1-2 |
DOIs | |
State | Published - 8 Feb 2019 |
All Science Journal Classification (ASJC) codes
- General Mathematics