A bound for the first cohomology of a projective surface
The paper under review concerns bounds on \(h^ 1({\mathcal O}_ X(n))\) for normal projective surfaces, in terms of the arithmetic genus of a generic hyperplane section. Two cases occur depending on whether \(h^ 2({\mathcal O}_ X)\) vanishes or not. The method is by chasing cohomology sequences.
arithmetic genus of a generic hyperplane section
scientific article; zbMATH DE number 4156627