RT info:eu-repo/semantics/article
T1 Castelnuovo–Mumford regularity of projective monomial curves via sumsets
A1 Giménez, Philippe Thierry
A1 González Sánchez, Mario
K1 Castelnuovo–Mumford regularity
K1 Projective monomial curve
K1 Semigroup ring
K1 Sumset
K1 Apery set
K1 12 Matemáticas
AB Let A={a0,…,an−1} be a finite set of n≥4 non-negative relatively prime integers, such that 0=a0<a1<⋯<an−1=d. The s-fold sumset of A is the set sA of integers that contains all the sums of s elements in A. On the other hand, given an infinite field k, one can associate with A the projective monomial curve CAparametrized by A,CA={(vd:ua1vd−a1:⋯:uan−2vd−an−2:ud)∣(u:v)∈P1k}⊂Pn−1k.The exponents in the previous parametrization of CAdefine a homogeneous semigroup S⊂N2. We provide several results relating the Castelnuovo–Mumford regularity of CA to the behavior of the sumsets of A and to the combinatorics of the semigroup S that reveal a new interplay between commutative algebra and additive number theory.
PB Springer
SN 1660-5446
YR 2023
FD 2023
LK https://uvadoc.uva.es/handle/10324/61604
UL https://uvadoc.uva.es/handle/10324/61604
LA eng
NO Mediterranean Journal of Mathematics, 2023, vol. 20, n. 5, art. 287
NO Producción Científica
DS UVaDOC
RD 11-jul-2024