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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Uniqueness of exceptional singular quartics
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by Karen A. Chandler
Proc. Amer. Math. Soc. 132 (2004), 347-352
DOI: https://doi.org/10.1090/S0002-9939-03-07153-3
Published electronically: June 23, 2003

Abstract:

We prove that given a general collection $\Gamma$ of 14 points of $\mathbb {P}^4=\mathbb {P}^4_\mathcal {K}$ ($\mathcal {K}$ an infinite field) there is a unique quartic hypersurface that is singular on $\Gamma$. This completes the solution to the open problem of the dimension of a linear system of hypersurfaces of $\mathbb {P}^n$ that are singular on a collection of general points.
References
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Bibliographic Information
  • Karen A. Chandler
  • Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
  • Email: kchandle@noether.math.nd.edu
  • Received by editor(s): April 17, 2001
  • Received by editor(s) in revised form: October 14, 2002
  • Published electronically: June 23, 2003
  • Communicated by: Michael Stillman
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 347-352
  • MSC (2000): Primary 14N10; Secondary 14C20
  • DOI: https://doi.org/10.1090/S0002-9939-03-07153-3
  • MathSciNet review: 2022355