7 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…

CSW's conjecture. Let $f_1,\ldots,f_s\in k[V]^G$ be the homogeneous invariant polynomials arising in the generic representation. Then

Let $(\boldsymbol{\omega}_i,\mathbf{v}_i)$, $1\leq i\leq 3$, be three screws, with $[\mathbf{a},\mathbf{b},\mathbf{c}]$ denoting the scalar triple product of three vectors. The Euc…

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 $S_n:=\mathbb{Q}[y_1,\dots,y_n]$ with the degree-lexicographic term order $\prec$ satisfying $y_1\succ y_2\succ\dots\succ y_n$. Assume the polynomiality conjecture, so that eve…

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…

Let $X_G$ be the del Pezzo surface of degree three associated with six generic linear forms, and let $\boldsymbol{\ell}=(\ell_1,\ell_2,\ldots,\ell_6)$ be generic. In the case $d=3$…