On minimal singular metrics of certain class of line bundles whose section ring is not finitely generated (Q5962660)

The main result in this paper is the existence of smooth Hermitian metrics, with semi-positivity curvature, on a line bundle over the blow-up of the projective plane at twelve points, also called Zariski's example. This line bundle is nef, big, not semi-ample and has section ring not finitely generated. Moreover is proved the existence of a smooth Hermitian metric with semi-positive curvature on a generalization of Zariski's example pointed out by Mumford. From the main theorem in this paper we can expect the description of minimal singular metrics of a pseudo-effective line bundle not big.