Tropicalization of rational varieties via curve valuations

A DICKENSTEIN

Workshop; School on Tropical Moduli Spaces; 2021

Institut Mittag-Leffler, Suecia

Weaddress the description of the tropicalization of families of rationalvarieties under parametrizations with prescribed support, via curve valuations.We recover and extend results by Sturmfels, Tevelev and Yu for genericcoefficients, considering rational parametrizations with non-trivialdenominator. The advantage of our point of view is that it can be generalizedto deal with non-generic parametrizations. We provide a detailed analysis ofthe degree of the closed image,  based oncombinatorial conditions on the relative positions of the supports of thepolynomials defining the parametrization.  We obtain a new formula and finer bounds onthe degree, when the supports of the  polynomialsare different. We also present a new formula and bounds for the order at theorigin in case the closed image is a hypersurface.