12 problems

Let $G\subset \operatorname{SL}(3,\mathbb{C})$ be a finite subgroup, let $Y=G\operatorname{-Hilb}(\mathbb{C}^{3})$, and let $\mathcal{R}_{k}$ be the tautological bundle on $Y$ asso…

Let $C$ be a smooth projective curve, let $E$ be a vector bundle on $C$ with $\operatorname{rk} E\ge 2$, and let $\operatorname{Quot}_d(E)$ be the punctual Quot scheme of length-…

Dualized exterior-power vanishing conjecture.

Symmetric-power conjecture. For every $k\leq n+r(a+1)$,

Exterior-power conjecture. For every $k\leq n+r(a+1)$,

Let $F$ be a $(k-1)$-very ample bundle of rank $r$ on an Enriques surface. Write … where $v=v(F)=\operatorname{ch}(F)\sqrt{\operatorname{Td}(X)}$ is the Mukai vector. Improved boun…

Let $S$) be a smooth connected surface with $h^1(O_S)=0$ whose Picard group is generated by line bundles $\mathcal{L}_1,\cdots,\mathcal{L}_m$. Consider a line bundle…

Marian–Oprea–Pandharipande conjecture. The universal series are

Finite Quot tautological Chern-class conjecture. One has

Universal-series correspondence. The series satisfy

Let $Y$ be a smooth variety and let $E$ be a vector bundle of arbitrary rank on $Y$. Let $E^{[n]}$ denote its tautological bundle on the Hilbert scheme $Y^{[n]}$, and let formula ……

Wang's conjecture. One has