Uniqueness of exceptional singular quartics
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- by Karen A. Chandler PDF
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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.References
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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
- 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