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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On flat families of fat points
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by Giuseppe Paxia PDF
Proc. Amer. Math. Soc. 112 (1991), 19-23 Request permission

Abstract:

The aim of this paper is to fill a gap in a proof of a theorem by B. Segre regarding the regularity of linear systems of curves in ${P^2}$. This is done by showing that some subschemes of "fat points" of ${P^2}$ form a flat family over an integral quasiprojective variety of which we give an explicit construction.
References
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  • Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
  • Joe Harris, Curves in projective space, Séminaire de Mathématiques Supérieures [Seminar on Higher Mathematics], vol. 85, Presses de l’Université de Montréal, Montreal, Que., 1982. With the collaboration of David Eisenbud. MR 685427
  • Beniamino Segre, Alcune questioni su insiemi finiti di punti in geometria algebrica, Univ. e Politec. Torino Rend. Sem. Mat. 20 (1960/61), 67–85 (Italian). MR 169119
  • Edoardo Sernesi, Topics on families of projective schemes, Queen’s Papers in Pure and Applied Mathematics, vol. 73, Queen’s University, Kingston, ON, 1986. MR 869062
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 112 (1991), 19-23
  • MSC: Primary 14C05; Secondary 14C20, 14H10
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1055777-6
  • MathSciNet review: 1055777