All Questions

I heard once about one open problem. That was about existing a hypersurface of a small degree (5? or 6?) passing through some number (5? 6?) of 3-fold points and 2-fold lines (3 lines?). It was said ...

Throughout, singular Del Pezzo means a surface with only isolated singularities and ample anti-canonical divisor. Suppose $X$ is a singular Del Pezzo of degree 2 over a field $k$ where $\text{char}(k)\...

Let $f:\mathbb{C}^2 \to \mathbb{C}^2/G$ be a quotient surface singularity. What properties should $G$ have such that the pushforward $f_*\mathcal{O}_{\mathbb{C}^2}$, of the structure sheaf $\mathcal{O}...