Unboundedness of Markov complexity of monomial curves in An for n ≥ 4

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Kosta, Dimitra¹  Thoma, Apostolos² 

[1] Univ Glasgow, Sch Math & Stat, Univ Pl, Glasgow G12 8SQ, Lanark, Scotland

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

关键词: Toric ideals;    Markov basis;    Monomial curves;    Lawrence liftings;   

DOI  :  10.1016/j.jpaa.2019.106249

来源: Elsevier

【 摘 要 】

Computing the complexity of Markov bases is an extremely challenging problem; no formula is known in general and there are very few classes of toric ideals for which the Markov complexity has been computed. A monomial curve C in A(3) has Markov complexity m(C) two or three. Two if the monomial curve is complete intersection and three otherwise. Our main result shows that there is no d is an element of N such that m(C) <= d for all monomial curves C in A(4). The same result is true even if we restrict to complete intersections. We extend this result to all monomial curves in A(n), where n >= 4. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free