2020/10/05 by Alicia Dickenstein, María Isabel Herrero, Dickenstein, Alicia +4
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Applied mathematics #Artificial intelligence #Commutative Algebra (math.AC) #Computer science #Degree (music) #FOS: Mathematics #Geometry #Hypersurface #Image (mathematics) #Mathematical analysis #Mathematics #Order (exchange) #Parametrization (atmospheric modeling) #Point (geometry) #Polynomial #Polynomial and algebraic computation #Pure mathematics #Tensor decomposition and applications #math.AC #math.AG
paper · pdf · doi:10.48550/arxiv.2010.02093
arxiv created 2020/10/05 · openalex publication_date 2020/10/05 · arxiv updated 2020/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We address the description of the tropicalization of families of rational varieties under parametrizations with prescribed support, via curve valuations. We recover and extend results by Sturmfels, Tevelev and Yu for generic coefficients, considering rational parametrizations with non-trivial denominator. The advantage of our point of view is that it can be generalized to deal with non-generic parametrizations. We provide a detailed analysis of the degree of the closed image, based on combinatorial conditions on the relative positions of the supports of the polynomials defining the parametrization. We obtain a new formula and finer bounds on the degree, when the supports of the polynomials are different. We also present a new formula and bounds for the order at the origin in case the closed image is a hypersurface.