6 problems

Let $X$ be a compact complex manifold of dimension $d$, and let $(\eta_{d-1},\eta_{d-2})$ be a pair of cohomology classes of bidegrees $(d-1,d-1)$ and $(d-2,d-2)$, respectively. A…

A Hodge-Riemann pair is a pair of cohomology classes $(\eta_{d-1},\eta_{d-2})$ satisfying the Hodge-Riemann relations, while a Bogomolov pair is a pair for which semistability with…

Restriction conjecture. The restriction $E|_D$ remains $\ell$-(semi)stable for $a\gg0$.

Let $\mathcal{M}(14)$ be the moduli space considered in the paper, and let $\mathfrak{V}$ be the constructed generically non-reduced component containing $\overline{\mathcal{C}}$.…

Let $S$ be a smooth projective surface, let $P^\perp_{\alpha}(n)$ be the Joyce–Song pair invariant for charge $\alpha=(r,c_1(L),c_2)$, and let $\chi(\alpha(n))$ denote the relevant…

Let $cal F$ be a semistable sheaf on $cmathbb{P}^2$ with Hilbert polynomial $P(t)=rt+chi$, where $r e 1$ and $0leqchi<r$ are integers. If $h^1(mathcal F)0$, then … with equality on…