3 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 $K^2$ denote the self-intersection of the canonical class of a smooth projective surface, and let $\chi=\chi(\mathcal O_S)$ be its holomorphic Euler characteristic. Zappa's con…

Let $X$ be a minimal surface of general type and maximal Albanese dimension with irregularity $q\geq 4$. Manetti's geography conjecture. One should have … This inequality concerns…