2 problems

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Sidman–Smith conjecture on determinantal ideals of cactus varieties
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…
Conjecturesolvedcactus-varieties determinantal-ideals secant-varietiesarXiv posted 2 days ago
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Component correspondence for Grassmann cactus varieties and Hilbert schemes
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…
Conjectureopencactus-varieties hilbert-schemes projective-geometryarXiv posted 2 days ago

Sidman–Smith conjecture on determinantal ideals of cactus varieties