2 problems

Let $X$ be a smooth projective variety of dimension $n$. Let $\kappa_k(X,L)$ be the $k$-th cactus variety, namely the closure of the union of the $k$-planes spanned by finite subsc…

Component correspondence conjecture. The irreducible components of $\mathfrak{K}_{r,k}(X)$ are in bijection with the irreducible components of $\operatorname{Hilb}_r(X)$ whose gene…