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TitleComplete intersections in simplicial toric varieties
Author(s) Isabel Bermejo, Ignacio García-Marco
TypeArticle in Journal
AbstractAbstract Given a set A = a 1 , , a n ⊂ N m of nonzero vectors defining a simplicial toric ideal I A ⊂ k [ x 1 , , x n ] , where k is an arbitrary field, we provide an algorithm for checking whether I A is a complete intersection. This algorithm does not require the explicit computation of a minimal set of generators of I A . The algorithm is based on the application of some new results concerning toric ideals to the simplicial case. For homogeneous simplicial toric ideals, we provide a simpler version of this algorithm. Moreover, when k is an algebraically closed field, we list all ideal-theoretic complete intersection simplicial projective toric varieties that are either smooth or have one singular point.
KeywordsComplete intersection, Simplicial toric ideal, Singularities, Algorithm
URL http://www.sciencedirect.com/science/article/pii/S0747717114000881
JournalJournal of Symbolic Computation
Volume68, Part 1
Pages265 - 286
Translation No
Refereed No