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.
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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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Communicated by Siamak Yassemi.
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Haghighi, H., Mosakhani, M. All Fat Point Subschemes in \({\mathbb {P}}^2\) with the Waldschmidt Constant Less than 5 / 2. Bull. Malays. Math. Sci. Soc. 43, 3221–3228 (2020). https://doi.org/10.1007/s40840-019-00865-y
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DOI: https://doi.org/10.1007/s40840-019-00865-y