Complete intersections in simplicial toric varieties. (May 2015)

• Record Type: Journal Article
• Authors: Bermejo, Isabel; García-Marco, Ignacio
• Is Part Of: Journal of symbolic computation. Volume 68:Part 1(2015)
• Page Start: 265
• Page End: 286
• Publication Date: 2015-05
• Subjects: Complete intersection -- Simplicial toric ideal -- Singularities -- Algorithm; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2014.09.020
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: 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.