8 problems

Let $L\subseteq\mathbb{P}^n$ be a linear subspace of dimension $d$ not contained in any coordinate hyperplane, let $M=\operatorname{M}(L)$, and let $F$ be a flat of $M$. Write…

Let $n=qp$ and let $I=\langle f_0,f_1,\ldots,f_{p-1}\rangle\cap R^{S_n}$ be the elimination ideal, where the $f_i$ are the polynomials obtained by collecting the coefficients of th…

Dilation elimination conjecture. One has

Elimination ideal conjecture. One has

Let $f(x_1,\ldots,x_n)$ be a generic form, and let $\Delta(f)$ denote its multivariate discriminant. Let ${\tt Hp}(f,[x_n,\ldots,x_1])$ be the polynomial associated with the iterat…

Recursive elimination conjecture. For arbitrary $n$,

Let $f_1,f_2$ define two affine plane curves, and let $g$ generate their elimination ideal in the $y$-coordinate, while $R$ denotes their resultant with respect to $x$. Assume that…

Arbitrary-degree elimination conjecture. For arbitrary $n$, $L$ has projective dimension two and specializes to the defining ideal of the Rees algebra $\mathcal R$.