10 problems

Let $X$ and $Y$ be algebraic K3 surfaces with transcendental lattices $T_X$ and $T_Y$, and let $calpha\in\operatorname{Br}(X)$ and $\beta\in\operatorname{Br}(Y)$. Regard…

Let $X$ be a complex variety and let $H^2(X,\mathcal{O}_X^*)$ classify holomorphic gerbes. The Brauer group consists of the elements arising from holomorphic locally free twisted s…

Let $E$ be a sheaf of positive rank $r$, set $F=E\otimes\det(E)^{-1/r}$, and identify the obstruction space for deforming the associated $\mu_r$-twisted sheaf $F$ with … Here…

Let $X$ be a quasi-separated Deligne–Mumford stack with generically trivial stabilizer. Let $\mathcal{M}\in \operatorname{QCoh}(X)$ and let $\alpha\in \mathrm{Br}(X)$. Write…

Let $\pi:{{{{{{{{\mathcal M}}}}}}}}\rightarrow S$ be a deformation of a smooth complex projective variety $M_0$ over a smooth germ $(S,0)$, and write $M_s=\pi^{-1}(s)$. Let…

Let $X$ be a singular Calabi–Yau threefold, let $\rho:\widehat{X}\to X$ be a non-Kähler small resolution, let $\alpha\in\operatorname{Br}(\widehat{X})$, and let $\widehat{X}'$ be a…

Let $X$ be a singular Calabi–Yau threefold, let $\rho:\widehat{X}\to X$ be a non-Kähler small resolution, and let $\alpha\in\operatorname{Br}(\widehat{X})$. Let $K(X)$ denote the K…

Let $\mathcal{E}$ be an $\alpha$-twisted locally free sheaf on $\operatorname{Spec}K$ of rank $n$, and let $\mathbb{P}\mathcal{E}$ denote its associated twisted projective space. T…

Jiang's twisted multiple-cover conjecture. If $H^{0,1}(S)=H^{0,2}(S)=0$, there exist rational numbers $\operatorname{VW}^{\operatorname{tw}}_{\alpha_i}({\mathfrak S})$ such that

Let $X$ be a scheme over an ordinary commutative ring $S$, let $p:X\rightarrow\operatorname{Spec} S$ be the structure morphism, and let $\alpha\in\operatorname{Br}(S)$. Write…