8 problems

Let Setup be fixed, let $v \colon P \to \mathbb{R}_{>0}$ be a weight, and let $\mathcal{E}$ be a reflexive sheaf of rank $r$ that is $v$-stable. Bogomolov–Gieseker conjecture. The…

Let $X$ be a smooth projective Calabi–Yau $4$-fold, let $\beta\in H_2(X,\mathbb{Z})$ be an irreducible curve class, and let $\gamma_1,\ldots,\gamma_l$ be integral cohomology classe…

Let $S$ be a del Pezzo surface with a smooth anticanonical divisor, and let $\beta$ be a curve class. The higher genus relative Gromov–Witten invariants of $S$ relative to the divi…

Let $S$ be a K3 surface, let $v=(r,\xi,a)\in H^{2*}(S,\mathbb{Z})$ be a Mukai vector, and let $\omega$ be a $v$-generic Kähler class satisfying the hypotheses under which the modul…

Douglas–Reinbacher–Yau conjecture. There exists a rank-$r$ stable reflexive sheaf $\mathcal E$ on $X$ with respect to some polarization such that $c_1(\mathcal E)=0$,…

Strong Bogomolov–Gieseker conjecture. One has

Stable-sheaf inequality conjecture. Then

Let $X$ be an abelian surface with $\operatorname{NS}(X)=\mathbb{Z} H$ and let $v$ be a Mukai vector with … Suppose that $v$ has at least one solution of the numerical equation. Am…