16 problems

Arrondo–Bernardi conjecture. The secant variety $\sigma_s(\operatorname{Split}_d(\mathbb P^n))$ is nondefective unless $d=2$ and $2\leq s\leq\frac{n}{2}$.

Let $C_{p,d}(\mathbb{P}^n)$ denote the Chow variety of effective algebraic $p$-cycles of degree $d$ in complex projective space, and let its Betti numbers be the ranks of its singu…

Let $C_{p,d}(\mathbb{P}^n)$ denote the Chow variety of effective algebraic $p$-cycles of degree $d$ in complex projective space, let $L_qH_k(-)_{\mathbb{Q}}$ denote Lawson homology…

Odd Betti number vanishing conjecture. All odd Betti numbers of $C_{p,d}({\mathbb{P}}^n)$ vanish; equivalently,

Hu's rational cycle class conjecture. For all $d\geq 0$ and $0\leq p\leq n$,

Hu's integral cycle class conjecture. For all $d\geq 0$ and $0\leq p\leq n$,

Let $M(m)$ be the matrix parametrizing twisted cubics as above, and let $\iota_{\mathrm{tw}}$ be the rational map from the constrained parameter space to the Chow variety of twiste…

Let $\boldsymbol d$ be a composition of the degree data, let $n$ be a nonnegative integer, and let $\operatorname{CV}_{\boldsymbol d}(\mathbb P^n)$ denote the corresponding Chow–Ve…

Let $C_{p,d}({\mathbb{P}}^n)$ denote the Chow variety of effective $p$-dimensional algebraic cycles of degree $d$ in projective space. Write $\operatorname{Ch}_q$ for the codimensi…

For integers $n\geq p\geq 0$ and $d\geq 0$, let $C_{p,d}({\mathbb{P}}^n)$ denote the Chow variety of effective $p$-dimensional algebraic cycles of degree $d$ in projective space, l…

Let $\Sigma_1,\Sigma_2\subset\mathbb{R}^{n+1}/\mathbb{R}$ be pure $(n-k-1)$-dimensional tropical varieties. For a tropical variety $\Sigma$, let $Z_\Sigma$ denote its tropical Chow…

Let $X\subset\mathbb{P}^n$ be an algebraic variety intersecting the torus $\operatorname{T}^n$, and let $Z_{\operatorname{Trop}(X)}$ denote the tropical Chow hypersurface associate…

Let $X\subset\mathbb{P}^n$ be a projective variety, and let $Z_X$ be its Chow hypersurface in the Grassmannian parametrizing projective linear spaces that intersect $X$. Its tropic…

Let $X\in \mathbb{P}W^*$ be an algebraic variety, let $\sigma_r(X)$ denote its $r$-th secant variety, and let $I_\delta(Y)$ denote the degree-$\delta$ component of the ideal of a v…

Let $V$ be a finite-dimensional complex vector space, and let … be the Foulkes–Howe map, whose kernel is the degree-$\delta$ component of the ideal of the Chow variety. Foulkes–How…

Chow-valued GW/DT conjecture. The equivalence of Corollary TChow, namely the equality of the corresponding Gromov–Witten and Donaldson–Thomas homological push-forwards after…