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

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

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 $ \mathbb{A}^3$ has Markov complexity $m(C)$  two or three. Two if the monomial curve is a complete intersection and three otherwise. Our main result shows that there is no $d \in \mathbb{N}$  such that  $m(C) \leq d$ for all monomial curves C in  $ \mathbb{A}^4$. The same result is true even if we restrict to complete intersections. We extend this result to all monomial curves in $ \mathbb{A}^n$, where $n \geq 4$.

Speaker

Dimitra Kosta, University of Edinburgh

How to attend

If not a member of the Dept. Mathematical Science at the University of Essex, you can register your interest in attending the seminar and request the Zoom’s meeting password by emailing Dr Dmitry Savostyanov (d.savostyanov@essex.ac.uk)