19 problems

Let $X$, $H$, $\Gamma$, $\mathcal{U}$, $\mathcal{A}^b(X)$, $\nu_{b,w}$, $\mathbf{v}_i^b$, $\overline{\Delta}$, and $\mathbf{ch}^{\gamma}_1$ be as in the paper, with…

Let $X$ be the threefold considered in the paper, let $H$ be the chosen ample divisor, and let…

Bayer–Macrì–Toda conjecture. There exists $546d53953c(X)_{4d9}$ with $546.Hd5390$ such that, for every $w>\frac{1}{2}b^2+534$ and every $539_{b,w}$-semistable object…

Let $X$ be the canonical line bundle of $\mathbb{P}^3$, with projection $\pi:X\to\mathbb{P}^3$. Let $\beta\in\mathbb{R}$ and let $\mathcal{E}$ be an exceptional locally free sheaf…

Let $X$ be the canonical line bundle of $\mathbb{P}^3$, with projection $\pi:X\to\mathbb{P}^3$, and let $H$ be the pullback of the hyperplane class. Let…

Let $(X,H)$ be a polarized smooth projective $3$-fold. For $b\bitin\mathbb{R}$ and $a>0$, let $\sigma_{a,b}=(\mathcal{A}^b,Z_{a,b})$ be the tilt-stability condition, and let…

Let $(X,H)$ be a smooth complex projective polarized variety. Let $\gamma=\gamma_{X,H}$ be a class as in the source's definition of $\gamma$, and let…

Let $X$ be a smooth projective threefold that is the complete intersection of a quadratic and a quartic hypersurface in $\mathbb{P}^5$, and let $H$ be an ample class. For…

Bayer–Macrì–Toda Bogomolov–Gieseker inequality. For any $(b,w)\in U$ and $\nu_{b,w}$-semistable $E\in\mathcal D(X)$, one has

Let $X$ be the smooth projective threefold under consideration, let $H$ be its ample divisor, and let $\beta$ and $m$ be the numerical data defining $v_n$. Set … Let the strong Bog…

Let $X$ be the smooth projective threefold under consideration, let $H$ be its ample divisor, and let $u{b,w}$ and $\mathcal A(b)$ be the tilt slope and heart defined above, with…

Fix real numbers $\alpha_0>0$ and $\beta_0$, and let $E\in\operatorname{Coh}^{\alpha_0\omega,B+\beta_0\omega}(X)$ be a $\nu_{\alpha_0\omega,B+\beta_0\omega}$-semistable object. Def…

Bayer–Macrì–Toda conjecture. For any $\nu_{\alpha,\beta}$-stable object $E\in\operatorname{Coh}^{\beta}(X)$ with $\nu_{\alpha,\beta}(E)=0$, the inequality

Bogomolov–Gieseker type conjecture. One should have

Limiting BG conjecture. Suppose there is an open neighborhood $U\subset\mathbb{R}^2$ containing $(0,\overline{\beta}(E))$ such that, for every $(\alpha,\beta)\in U$ with $\alpha>0$…

Bayer–Macrì–Stellari quadratic Bogomolov–Gieseker inequality conjecture. For every $\nu_{\omega,B}$-semistable object $E\in\mathcal{B}_{\omega,B}$,

Let $X$ be a smooth projective threefold. For an object $E\in D^b(X)$, let $\overline{\beta}(E)$ be the limiting value of the parameter $\beta$ associated with the kernel of the re…

Let $X$ be a smooth projective threefold and let $H\in\operatorname{NS}(X)$ be an ample class. For a real number $\beta$, write $\operatorname{ch}_i^\beta$ for the $\beta H$-twiste…

Let $X$ be a smooth projective threefold. Let $u{\omega,B}$ be the tilt slope on the tilted heart $\operatorname{Coh}^{\omega,B}(X)$, where $\omega$ is ample and $B$ is a real divisor…