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Nagata’s conjecture for a square or nearly-square number of points

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Abstract

In this paper we prove that a linear system of plane curves of degree d with n points of multiplicity m always has the expected dimension when n is a perfect square. We also prove some results on the dimension of the linear system when n is close to a perfect square.

Keywords: Interpolation, Nagata, Linear systems, Plane curves

Mathematics Subject Classification (2000): 14J26, 14N05

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Authors and Affiliations

  1. Dipartimento di Matematica, Universita’ di Roma Tor Vergata, Via della Ricerca Scientifica, 00133 Roma (Italia),  

    Ciro Ciliberto

  2. Department of Mathematics, Colorado State University, Fort Collins, CO 80523, USA

    Rick Miranda

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  1. Ciro Ciliberto
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  2. Rick Miranda
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Ciliberto, C., Miranda, R. Nagata’s conjecture for a square or nearly-square number of points. Ricerche mat. 55, 71–78 (2006). https://doi.org/10.1007/s11587-006-0005-y

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  • DOI: https://doi.org/10.1007/s11587-006-0005-y

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