Discrete behavior of Seshadri constants on surfaces

Abstract

Working over C, we show that, apart possibly from a unique limit point, the possible values of multi-point Seshadri constant for general points on smooth projective surfaces form a discrete set. In addition to its theoretical interest, this result is of practical value, which we demonstrate by giving significantly improved explicit lower bounds for Seshadri constants on P^2 and new results about ample divisors on blow ups of P^2 at general points.

14 pages, to appear in J. Pure App. Algebra

References in corpus (3)

• Seshadri constants on algebraic surfaces
• Degenerations of Planar Linear Systems
• Reduction method for linear systems of plane curves with base fat points

Cited by in corpus (9)

• Restrictions on Seshadri constants on surfaces
• Comparing powers and symbolic powers of ideals
• An inequality between multipoint Seshadri constants
• On the valuative Nagata conjecture
• Extended Okounkov bodies and multi-point Seshadri constants
• On finiteness of curves with high canonical degree on a surface
• On submaximal curves in fake projective planes
• Multi-point Seshadri constants on ruled surfaces
• Transcendental versions in C n of the Nagata conjecture