Resurgence and Waldschmidt constant of the ideal of a fat almost collinear subscheme in ℙ2

Hassan Haghighi; Mohammad Mosakhani; Mohammad Zaman Fashami

doi:10.2478/aupcsm-2018-0006

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Resurgence and Waldschmidt constant of the ideal of a fat almost collinear subscheme in ℙ2

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Volume 17 (2018): Issue 1 (December 2018)

By: Hassan Haghighi, Mohammad Mosakhani and Mohammad Zaman Fashami

Open Access

|Feb 2019

Abstract

Let Zn = p₀ + p₁ + ··· + pn be a configuration of points in ℙ², where all points pi except p₀ lie on a line, and let I(Zn) be its corresponding homogeneous ideal in 𝕂 [ℙ²]. The resurgence and the Waldschmidt constant of I(Zn) in [5] have been computed. In this note, we compute these two invariants for the defining ideal of a fat point subscheme Zn,c = cp₀ + p₁ +··· + pn, i.e. the point p₀ is considered with multiplicity c. Our strategy is similar to [5].

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Articles in this issue

DOI: https://doi.org/10.2478/aupcsm-2018-0006 | Journal eISSN: 2300-133X | Journal ISSN: 2081-545X

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Language: English

Page range: 59 - 65

Submitted on: Feb 26, 2018

Accepted on: Jun 6, 2018

Published on: Feb 23, 2019

Published by: Pedagogical University of Cracow

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

fat points,

containment problem,

symbolic power,

Waldschmidt constant,

resurgence

Related subjects:

Mathematics,

General mathematics

© 2019 Hassan Haghighi, Mohammad Mosakhani, Mohammad Zaman Fashami, published by Pedagogical University of Cracow
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 17 (2018): Issue 1 (December 2018)