RT info:eu-repo/semantics/doctoralThesis
T1 Syzygies, regularity, and their interplay with additive combinatorics
A1 González Sánchez, Mario
A2 Universidad de Valladolid. Escuela de Doctorado
K1 Algebra
K1 Graded free resolutions
K1 Resoluciones libres graduadas
K1 Additive combinatorics
K1 Combinatoria aditiva
K1 Castelnuovo-Mumford regularity
K1 Regularidad
K1 Conjuntos suma
K1 Sumsets
K1 12 Matemáticas
AB In this thesis, we study some interactions between commutative algebra and additive combinatorics. Based on recent works by Eliahou and Mazumdar, Elias, and Colarte-Gómez, Elias and Miró-Roig, we associate with each finite set A ⊂ ℕᵈ a projective toric variety  X⊂ ℙₖⁿ,  where k is an infinite field and n = |A|-1. We focus on the study of the sumsets of A and the Castelnuovo-Mumford regularity of [k], the coordinate ring of X. In particular, we look at the cases when X is a curve, a smooth variety, and a surface with a single singular point. Moreover, when X is a curve C, we study the relation between the Betti numbers of k [C] and its affine charts. Finally, we provide an explicit method to compute the minimal graded free resolution of R/I as A-module, where I ⊂ R = k[x₁,…,xₙ] is a weighted homogeneous ideal and A, the polynomial ring in the last d variables, is a Noether normalization of R/I.
YR 2025
FD 2025
LK https://uvadoc.uva.es/handle/10324/81884
UL https://uvadoc.uva.es/handle/10324/81884
LA spa
NO Escuela de Doctorado
DS UVaDOC
RD 20-ene-2026