The cone of curves associated to a plane configuration
The cone of curves or of effective divisors is a crucial object in modern algebraic geometry. Questions on singularities, morphisms, minimal models, moduli and many others are closely related to the investigation of the this cone for classes of varieties. The paper under review studies the cone of effective divisors of some blow ups of the projective plane. The result is a series of conditions on the polyhedrality of the cone of effective divisors of the blow up of \({\mathbb P^2}\) in valuations centered in a single point \(p\). The results are applied to singularities of plane curves and to low cardinality configurations.
scientific article; zbMATH DE number 2157819