3 problems

Let $X$ be a minimal surface of general type and maximal Albanese dimension. The Severi equality characterization states that … if and only if the canonical model of $X$ is a flat…

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…

Symmetric-product conjecture. The only irregular surface with no irrational pencil of genus greater than $1$ and $p_g=2q-3$ is the symmetric product of a genus-three curve.