7 problems

Kleppe–Ellia's conjecture. If $C$ is linearly normal, then every small deformation $C'$ of $C$ in $\mathbb P^3$ is contained in a cubic surface $S'\subset\mathbb P^3$; equivalently…

Universal k-equivalence descent conjecture. On the pair of pants, $k$-equivalence implies $(k-1)$-equivalence for all positive integers $k$.

The intersection-triple bound conjecture. For any curve $\alpha$ on the pair of pants,

Let $\mathcal{Q}$ be an acyclic quiver, let $P_{\mathcal{Q}}$ be the relevant set of seeds, and for each $\sigma\in P_{\mathcal{Q}}$ let $\Gamma_{\sigma}$ be the set of isotopy cla…

Let $R$ be the path algebra of an acyclic quiver, let $g$ be the onto map from admissible curves to indecomposable modules corresponding to positive real roots, and let $M$ be an i…

Let $X_n$ be the projective plane blown up at $n$ general points, and let $C$ be an irreducible curve of genus $g>0$ on $X_n$. Let $(3;1^9,0^{n-9})$ denote the indicated plane line…

Cobracket criterion conjecture. If