# Unboundedness of Markov complexity of monomial curves in A^n for n ≥ 4

Dimitra Kosta, Apostolos Thoma

Research output: Contribution to journalArticlepeer-review

## 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 $A^3$ has Markov complexity two or three. Two if the monomial curve is complete intersection and three otherwise. Our main result shows that there is no $d \in N$ such that $m(C) \leq d$ 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 $n \geq 4$.
Original language English 106249 12 Journal of pure and applied algebra 224 6 21 Oct 2019 https://doi.org/10.1016/j.jpaa.2019.106249 Published - Jun 2020

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