4 problems

Let $\mathbb{F}_e$ be a Hirzebruch surface and let $H_m$ be an arbitrary polarization. Let $\mathbf{v}\in K(\mathbb{F}_e)$ be a character such that there are $H_{\lceil m\rceil}$-p…

For each $d$, let $P_d(y)$ be the Poincaré polynomial of the corresponding moduli space, let $\widetilde P_{d,\chi}(y)$ be the Poincaré series of the stack of semistable sheaves, a…

Let $X$ be a Calabi-Yau manifold with Kähler metric. Let $L$ be an almost calibrated exact Lagrangian brane in $D^bFuk(X)$ with a Harder-Narasimhan decomposition … whose distinguis…

Let $(P,d\sigma)$ be the moment polytope of a polarised toric variety with canonical boundary measure $d\sigma$. A pair $(Q,d\sigma)$ is semistable when $\mathcal{L}_A(f)\geq 0$ fo…