6 problems

Effective linearization conjecture.

Good postulation conjecture. A finite union of general codimension $2$ linear subspaces in $\mathbb P^N$ has good postulation.

Conjecture B. There exists a function $c(r,d)$ such that

Let $\mathbf{k}$ be a perfect field and let $X\subset {\mathbb P}^N$ be a hypersurface of degree $d$ defined over $\mathbf{k}$ and containing a linear subspace $L$ defined over…

Let $\mathbb{H}^n=\{0,1\}^n$ be the vertices of the $n$-dimensional hypercube, and let $H(n,k)$ be the set of intersection sizes $|\mathbb{H}^n\cap S|$ as $S$ ranges over the $k$-d…

Melo–Winter's large-intersection conjecture.