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We prove that given a general collection Γ of 14 points of P 4 = P 4 K (K an infinite field) there is a unique quartic hypersurface that is singular on Γ. This completes the solution to the open problem of the dimension of a linear system of hypersurfaces of P n that are singular on a collection of general points.doi:10.1090/s0002-9939-03-07153-3 fatcat:gunctq22kzfg5az7zzuraayblm