3 problems

Let $G(m,n)$ denote the Grassmannian, and let a universal Sagbi basis mean a finite generating set that is a Sagbi basis for every monomial order. Finite universal Sagbi basis conj…

SatSAGBI termination conjecture. If there is a finite $\sigma$-SAGBI basis of $S:a_0^\infty$, then Procedure terminates in a finite number of iterations, hence it is an algorithm.…

Let $G=({\bf Z}/p)^r=\langle e_1,\ldots,e_r\rangle$ and let $V$ be the generic three-dimensional representation over $\mathbf{k}=\mathbf{F}_p(x_{1j},x_{2j}\mid j=1,\ldots,r)$. Defi…