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TitleVanishing ideals over complete multipartite graphs
Author(s) Jorge Neves, Maria Vaz Pinto
TypeArticle in Journal
AbstractAbstract We study the vanishing ideal of the parametrized algebraic toric set associated to the complete multipartite graph G = K_α_1 , … , α_r over a finite field of order q. We give an explicit family of binomial generators for this lattice ideal, consisting of the generators of the ideal of the torus (referred to as type I generators), a set of quadratic binomials corresponding to the cycles of length 4 in G and which generate the toric algebra of G (type II generators) and a set of binomials of degree q − 1 obtained combinatorially from G (type III generators). Using this explicit family of generators of the ideal, we show that its Castelnuovo–Mumford regularity is equal to max α_1 ( q − 2 ) , … , α_r ( q − 2 ) , ⌈ ( n − 1 ) ( q − 2 ) / 2 ⌉ , where n = α_1 + ⋯ + α_r .
ISSN0022-4049
URL http://www.sciencedirect.com/science/article/pii/S0022404913002090
LanguageEnglish
JournalJournal of Pure and Applied Algebra
Volume218
Number6
Pages1084 - 1094
Year2014
Edition0
Translation No
Refereed No
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