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All Fat Point Subschemes in \({\mathbb {P}}^2\) with the Waldschmidt Constant Less than 5 / 2

  • Hassan HaghighiEmail author
  • Mohammad Mosakhani
Article
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Abstract

Let \({\mathscr {A}}=m_1p_1+ \cdots +m_np_n\) be a fat point subscheme of \({\mathbb {P}}^2\), and let \(I({\mathscr {A}})\), which is called a fat point ideal, be its corresponding ideal in \({\mathbb {K}}[{\mathbb {P}}^2]\). In this note, we identify those fat point ideals in \({\mathbb {K}} [{\mathbb {P}}^2]\) for which their Waldschmidt constants are less than 5 / 2.

Keywords

Configuration of points Star configuration Symbolic power Waldschmidt constant Fat points 

Mathematics Subject Classification

Primary 14N20 13A02 Secondary 14N05 13F20 

Notes

Acknowledgements

We would like to thank the anonymous referee for her/his careful reading of this manuscript, valuable suggestions and making helpful remarks. These all helped to improve the manuscript. This paper was prepared based on a research project supported by K.N. Toosi University of Technology research council and Iran National Science Foundation (INSF) Grant No. 97008366.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.Faculty of MathematicsK. N. Toosi University of TechnologyTehranIran

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