Markov complexity of monomial curves

JOURNAL OF ALGEBRA

卷:417

Article

Charalambous, Hara¹  Thoma, Apostolos²  Vladoiu, Marius^3,4 

[1] Aristotle Univ Thessaloniki, Dept Math, Thessaloniki 54124, Greece

[2] Univ Ioannina, Dept Math, GR-45110 Ioannina, Greece

[3] Univ Bucharest, Fac Math & Comp Sci, Bucharest 010014, Romania

[4] Acad Romana, Simion Stoilow Inst Math, Res Grp, Project ID PCE 2011 3 1023, Bucharest 014700, Romania

关键词: Toric ideals;    Markov basis;    Graver basis;    Lawrence liftings;   

DOI  :  10.1016/j.jalgebra.2014.06.025

来源: Elsevier

【 摘 要 】

Let A = {a(1),...,a(n)} subset of N-m. We give an algebraic characterization of the universal Markov basis of the toric ideal I-A. We show that the Markov complexity of A = {n(1), n(2), n(3)} is equal to 2 if I-A is complete intersection and equal to 3 otherwise, answering a question posed by Santos and Sturmfels. We prove that for any r >= 2 there is a unique minimal Markov basis of A((r)). Moreover, we prove that for any integer l there exist integers n(1), n(2), n(3) such that the Graver complexity of A is greater than l. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free