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2019 Seshadri constants and special configurations of points in the projective plane
Piotr Pokora
Rocky Mountain J. Math. 49(3): 963-978 (2019). DOI: 10.1216/RMJ-2019-49-3-963

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.

Citation

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Piotr Pokora. "Seshadri constants and special configurations of points in the projective plane." Rocky Mountain J. Math. 49 (3) 963 - 978, 2019. https://doi.org/10.1216/RMJ-2019-49-3-963

Information

Published: 2019
First available in Project Euclid: 23 July 2019

zbMATH: 07088346
MathSciNet: MR3983310
Digital Object Identifier: 10.1216/RMJ-2019-49-3-963

Subjects:
Primary: 14C20, 14N20, 52C30

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 3 • 2019
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