<abstract xmlns="http://www.w3.org/1999/xhtml">Let <italic>Zn</italic> = <italic>p</italic>0 + <italic>p</italic>1 + <italic>···</italic> + <italic>pn</italic> be a configuration of points in ℙ2, where all points <italic>pi</italic> except <italic>p</italic>0 lie on a line, and let <italic>I</italic>(<italic>Zn</italic>) be its corresponding homogeneous ideal in 𝕂 [ℙ2]. The resurgence and the Waldschmidt constant of <italic>I</italic>(<italic>Zn</italic>) in [5] have been computed. In this note, we compute these two invariants for the defining ideal of a fat point subscheme <italic>Zn,c</italic> = <italic>cp</italic>0 + <italic>p</italic>1 +<italic>···</italic> + <italic>pn</italic>, i.e. the point <italic>p</italic>0 is considered with multiplicity <italic>c</italic>. Our strategy is similar to [5].</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].

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

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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

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...

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

Published Online: Feb 23, 2019

Page range: 59 - 65

Received: Feb 26, 2018

Accepted: Jun 06, 2018

DOI: https://doi.org/10.2478/aupcsm-2018-0006

Keywords
fat points, containment problem, symbolic power, Waldschmidt constant, resurgence

© 2018 Hassan Haghighi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Feb 23, 2019

Page range: 59 - 65

Received: Feb 26, 2018

Accepted: Jun 06, 2018

DOI: https://doi.org/10.2478/aupcsm-2018-0006

Keywordsfat points, containment problem, symbolic power, Waldschmidt constant, resurgence

© 2018 Hassan Haghighi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Keywords
fat points, containment problem, symbolic power, Waldschmidt constant, resurgence