On the degree of curves with prescribed multiplicities and bounded negativity

Abstract

We provide a lower bound on the degree of curves of the projective plane ${\mathbb{P}}^2$ passing through the centers of a divisorial valuation $\nu$ of ${\mathbb{P}}^2$ with prescribed multiplicities, and an upper bound for the Seshadri-type constant of $\nu$, $\hat{\mu }(\nu )$, constant that is crucial in the Nagata-type valuative conjecture. We also give some results related to the bounded negativity conjecture concerning those rational surfaces having the projective plane as a relatively minimal model.

Cited by in corpus (1)

• On the valuative Nagata conjecture