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Proceedings of the American Mathematical Society

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

 

 

Uniqueness of exceptional singular quartics


Author: Karen A. Chandler
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
Published electronically: June 23, 2003
MathSciNet review: 2022355
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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.


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Additional Information

Karen A. Chandler
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: kchandle@noether.math.nd.edu

DOI: https://doi.org/10.1090/S0002-9939-03-07153-3
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
Article copyright: © Copyright 2003 American Mathematical Society