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Publication - Dr Farhad Babaee

    Convexity of complements of tropical varieties, and approximations of currents

    Citation

    Adiprasito, K & Babaee, F, 2018, ‘Convexity of complements of tropical varieties, and approximations of currents’. Mathematische Annalen.

    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.

    Full details in the University publications repository