2 problems

Let $S$ be a minimal smooth surface with geometric genus $p_g=4$ and birational canonical map, so that $S$ is a simple canonical surface. Write $K^2$ for the self-intersection of i…

Let $S\subset\mathbb{P}^5$ be a canonical surface, and let $d=\deg(S)$. Degree bound conjecture. There are no canonical surfaces of degree $d\geq 19$ in $\mathbb{P}^5$. This is pre…