Discrete behavior of Seshadri constants on surfaces

Brian Harbourne; Joaquim Roé

doi:https://doi.org/10.1016/j.jpaa.2007.06.018

Discrete behavior of Seshadri constants on surfaces

Brian Harbourne, Joaquim Roé

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

11 Citations (Scopus)

Abstract

Working over C, we show that, apart possibly from a unique limit point, the possible values of multi-point Seshadri constants 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 P2 and new results about ample divisors on blow ups of P2 at general points. © 2007 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	616-627
Journal	Journal of Pure and Applied Algebra
Volume	212
DOIs	https://doi.org/10.1016/j.jpaa.2007.06.018
Publication status	Published - 1 Mar 2008

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title = "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 constants 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 P2 and new results about ample divisors on blow ups of P2 at general points. {\textcopyright} 2007 Elsevier Ltd. All rights reserved.",

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AU - Harbourne, Brian

AU - Roé, Joaquim

PY - 2008/3/1

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N2 - Working over C, we show that, apart possibly from a unique limit point, the possible values of multi-point Seshadri constants 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 P2 and new results about ample divisors on blow ups of P2 at general points. © 2007 Elsevier Ltd. All rights reserved.

AB - Working over C, we show that, apart possibly from a unique limit point, the possible values of multi-point Seshadri constants 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 P2 and new results about ample divisors on blow ups of P2 at general points. © 2007 Elsevier Ltd. All rights reserved.

U2 - https://doi.org/10.1016/j.jpaa.2007.06.018

DO - https://doi.org/10.1016/j.jpaa.2007.06.018

M3 - Article

VL - 212

SP - 616

EP - 627

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

ER -