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Special Line Arrangements in \({\mathbb {P}}^2\) and Waldschmidt Constant of their Singular Points

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Abstract

Let \(\mathcal {L}=\{L_1, \dots ,L_d\}\) be a line arrangement in the projective plane and let I be the defining ideal of the set of all singular points of the union of lines in \(\mathcal {L}\). In this note, the Waldschmidt constant of I for some special cases of line arrangement \(\mathcal {L}\) is computed.

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Acknowledgements

We would like to thank the anonymous referee for her/his careful reading of the manuscript, valuable suggestions, and making many helpful remarks. All these helped to improve the manuscript.

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Authors and Affiliations

  1. Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran

    Hassan Haghighi & Mohammad Mosakhani

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  1. Hassan Haghighi
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  2. Mohammad Mosakhani
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Correspondence to Hassan Haghighi.

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Communicated by Rahim Zaare-Nahandi.

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Haghighi, H., Mosakhani, M. Special Line Arrangements in \({\mathbb {P}}^2\) and Waldschmidt Constant of their Singular Points. Bull. Iran. Math. Soc. 44, 1155–1161 (2018). https://doi.org/10.1007/s41980-018-0078-x

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  • DOI: https://doi.org/10.1007/s41980-018-0078-x

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