Description
Title: Unboundedness of Markov Complexity of monoidal curves in affine nspace for n at least 4Abstract:
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 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 $\mathbb{A}^4$. The same result is true even if we restrict to complete intersections. We extend this result to all monomial curves in $\mathbb{A}^n$, $n \geq 4$.
Period  11 Feb 2019 

Visiting from  Univ Glasgow (United Kingdom) 
Visitor degree  PhD 
Degree of Recognition  Local 
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Department of Mathematics  Algebra Seminar Series
Activity: Participating in or organising an event › Seminar/workshop/course