03/07/2012, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Maria Vaz Pinto, Instituto Superior Técnico
The regularity and the vanishing ideal of parameterized codes associated to even cycles
Let $X$ be an algebraic toric set in a projective space over a finite field $K$, parametrized by the $s$ edges of a graph $G$. We give an explicit combinatorial description of a set of generators of the vanishing ideal of $X$, $I(X)$, when $G$ is an even cycle or a connected bipartite graph with pairwise vertex disjoint even cycles. We also show a formula for the regularity of $S/I(X)$, where $S$ is a polynomial ring in $s$ variables over $K$.
