Linear Systems of Cubics Singular at General Points of Projective Space
Karen A. Chandler · Compositio Mathematica · 2002
We present an elementary proof that given a general collection of d points in P n the linear system of cubics singular on each point has the expected codimension except when n =4 and d =7. In that case the cubic is unique. This, together with previous work of the author, gives a proof of the Alexander–Hirschowitz interpolation theorem.