6 problems

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…

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…

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…