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.

References in corpus (8)

• Negative curves on algebraic surfaces
• Bounded Negativity and Arrangements of Lines
• Vanishing sequences and Okounkov bodies
• Bounded negativity, Harbourne constants and transversal arrangements of curves
• Non-positive and negative at infinity divisorial valuations of Hirzebruch surfaces
• Harbourne constants and conic configurations on the projective plane
• Harbourne constants, pull-back clusters and ramified morphisms
• Discrete equivalence of non-positive at infinity plane valuations

Cited by in corpus (1)

• On the valuative Nagata conjecture