11 problems

Ruled-surface characterization. There exists a counterexample to the Kawamata–Viehweg vanishing theorem on some geometrically ruled surface over $C$ if and only if $C$ is a Tango c…

Parabolic stability necessity conjecture. If $\widehat M$ admits a scalar-flat Kähler metric, then $E$ must be parabolically stable. This is a necessary-condition conjecture for th…

Let $M$ be a blown-up ruled surface of genus at least $2$, and let $[\omega]$ be an admissible Kähler class, meaning that $c_1\cup[\omega]=0$. Associate to $[\omega]$ its correspon…

Let $M$ be a ruled compact complex surface, and let $\widetilde{M}$ be its blow-up at sufficiently many points. Blow-up conjecture. The surface $\widetilde{M}$ admits a scalar-flat…

Let $X$) be the minimal ruled surface considered in the paper, with distinguished sections $S_0$ and $S_\infty$, and let $\omega$ be a conical higher cscK metric on $X$ with cone a…

Let $\mathbb{F}_e$ be the $e$-th Hirzebruch surface, with $C_e$ denoting its negative section. Let $P=\{p_1,\dots,p_r\}\subset \mathbb{F}_e$ be $r$ points in very general position,…

Self-intersection conjecture. One has

Sols and Sols' conjecture. If

Let $M_g=\Sigma_g\times S^2$ be a minimal topologically trivial ruled surface equipped with a symplectic form $\omega$. A symplectomorphism of $(M_g,\omega)$ is symplectically isot…

Let $\Sigma_{g,\ell}$ be a ruled surface over a Riemann surface $C_g$ of genus $g>0$, with fibre $f$. Let $r\geq 1$, $c_1$ be a first Chern class, and let…

Soit $K$ un corps global et soit $V$ une surface projective, lisse et géométriquement réglée sur $K$. Avec $\cyr{X}\mathcal N(V)$ défini comme le noyau de la restriction de…