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On flat families of fat points


Author: Giuseppe Paxia
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
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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 [Enhancements On Off] (What's this?)

  • [B-G] M. Boratinsky and S. Greco, Hilbert functions and Betti numbers in a flat family, Ann. Mat. Pura Appl. (4) 142 (1985), 277-292. MR 839041 (88b:14008)
  • [H1] R. Hartshorne, Algebraic geometry, Graduate Texts in Math., vol. 52, Springer, New York and Berlin, 1977. MR 0463157 (57:3116)
  • [H2] J. Harris, Curves in the projective space, Sem. Math. Sup., Presses Univ. Montréal, Montreal, PQ, 1982. MR 685427 (84g:14024)
  • [S] B. Segre, Alcune questioni su insiemi finiti di punti in geometria algebrica, Atti Convegno Intern. di Torino, 1961. MR 0169119 (29:6372)
  • [Se] E. Sernesi, Topics on families of projective schemes, Queen's Papers in Pure and Appl. Math., vol. 73, Queen's Univ., Kingston, ON, 1986. MR 869062 (88b:14006)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1055777-6
Article copyright: © Copyright 1991 American Mathematical Society

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