Tropically unirational varieties

Abstract

Abstract. We introduce tropically unirational varieties, which are subvarieties of tori that admit dominant rational maps whose tropicalisation is surjective. The central (and unresolved) question is whether all unirational varieties are tropically unirational. We present several techniques for proving tropical unirationality, along with various examples.

Linear and Rational Factorization of Tropical Polynomials

“…Tropical division is a highly non-trivial operation even in one variable [KLT15,Tsa12]. At the same time, it is a very useful operation: tropical rational polynomials have appeared in a variety of applications, from product-mix auctions in economics [BGK16], topological data analysis [Ver16], to unirational varieties [DF13] and ultra discrete equations [KLT15]. In general, the extension from N[S] to Z[S] parallels the extension from Minkowski sums to signed Minkowski sums.…”