Rocky Mountain Journal of Mathematics

Seshadri constants and special configurations of points in the projective plane

Piotr Pokora

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Abstract

In the present note, we focus on certain properties of special curves that might be used in the theory of multi-point Seshadri constants for ample line bundles on the complex projective plane. In particular, we provide three Ein-Lazarsfeld-Xu-type lemmas for plane curves and a lower bound on the multi-point Seshadri constant of $\mathcal {O}_{\mathbb {P}^{2}}(1)$ under the assumption that the chosen points are not very general. In the second part, we focus on certain arrangements of points in the plane which are given by line arrangements. We show that, in some cases, the multi-point Seshadri constants of $\mathcal {O}_{\mathbb {P}^{2}}(1)$ centered at singular loci of line arrangements are computed by lines from the arrangement having some extremal properties.

Article information

Source
Rocky Mountain J. Math., Volume 49, Number 3 (2019), 963-978.

Dates
First available in Project Euclid: 23 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1563847243

Digital Object Identifier
doi:10.1216/RMJ-2019-49-3-963

Mathematical Reviews number (MathSciNet)
MR3983310

Zentralblatt MATH identifier
07088346

Subjects
Primary: 14C20: Divisors, linear systems, invertible sheaves 14N20: Configurations and arrangements of linear subspaces 52C30: Planar arrangements of lines and pseudolines

Keywords
Seshadri constants point configurations projective plane

Citation

Pokora, Piotr. Seshadri constants and special configurations of points in the projective plane. Rocky Mountain J. Math. 49 (2019), no. 3, 963--978. doi:10.1216/RMJ-2019-49-3-963. https://projecteuclid.org/euclid.rmjm/1563847243


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