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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
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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 
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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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