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

Kosta, D. and Thoma, A. (2020) Unboundedness of Markov complexity of monomial curves in An for n ≥ 4. Journal of Pure and Applied Algebra, 224(6), 106249. (doi: 10.1016/j.jpaa.2019.106249)

Abstract

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 A3 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 ∈ N such that m(C) ≤ d for all monomial curves C in . The same result is true even if we restrict to complete intersections. We extend this result to all monomial curves in An, where n ≥ 4.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Kosta, Dr Dimitra
• Authors: Kosta, D., and Thoma, A.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Pure and Applied Algebra
• Publisher: Elsevier
• ISSN: 0022-4049
• ISSN (Online): 1873-1376
• Published Online: 21 October 2019
• Copyright Holders: Copyright © 2019 Elsevier
• First Published: First published in Journal of Pure and Applied Algebra 224(6):106249
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher