Fibers of Tropicalization
نویسنده
چکیده
We use functoriality of tropicalization and the geometry of projections of subvarieties of tori to show that the fibers of the tropicalization map are dense in the Zariski topology. For subvarieties of tori over fields of generalized power series, points in each tropical fiber are obtained “constructively” using Kedlaya’s transfinite version of Newton’s method.
منابع مشابه
Faithful Tropicalization of the Grassmannian of Planes
We show that the tropical projective Grassmannian of planes is homeomorphic to a closed subset of the analytic Grassmannian in Berkovich’s sense by constructing a continuous section to the tropicalization map. Our main tool is an explicit description of the algebraic coordinate rings of the toric strata of the Grassmannian. We determine the fibers of the tropicalization map and compute the init...
متن کاملTropicalization and Irreducibility of Generalized Vandermonde Determinants
We find geometric and arithmetic conditions in order to characterize the irreducibility of the determinant of the generic Vandermonde matrix over the algebraic closure of any field k. We also characterize those determinants whose tropicalization with respect to the variables of a row is irreducible.
متن کاملA dissertation submitted in partial satisfaction of the requirements for
Tropical Geometry by David E Speyer Doctor of Philosophy in Mathematics University of California, Berkeley Professor Bernd Sturmfels, Chair Let K be an algebraically closed field complete with respect to a nonarchimedean valuation v : K∗ → R. The reader should think ofK as the field of Puiseux series, ⋃∞ n=1 C((t )) and v as the map that assigns to a power series the exponent of its lowest degr...
متن کاملThe Tropicalization of the Moduli Space of Curves
We show that the skeleton of the Deligne-MumfordKnudsen moduli stack of stable curves is naturally identified with the moduli space of extended tropical curves, and that this is compatible with the “naive” set-theoretic tropicalization map. The proof passes through general structure results on the skeleton of a toroidal Deligne-Mumford stack. Furthermore, we construct tautological forgetful, cl...
متن کاملTropicalization of systems biology models
Systems biology use networks of biochemical reactions as models for cellular process. The dynamics of reaction networks with many well separated time scales, is well captured by asymptotic models obtained by tropicalization of the smooth dynamics, via the Litvinov-Maslov correspondence principle. The tropicalized models can be used to check the global stability and to identify sensitive paramet...
متن کامل