Uniqueness of exceptional singular quartics

Chandler, Karen

doi:10.1090/S0002-9939-03-07153-3

Uniqueness of exceptional singular quartics
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by Karen A. Chandler PDF

Proc. Amer. Math. Soc. 132 (2004), 347-352 Request permission

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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