  Secant varieties to Veronese embeddings of projective space are classical
varieties whose equations are not completely understood. Minors of
catalecticant matrices furnish some of their equations, and in some situations
even generate their ideals. Geramita conjectured that this is the case for the
secant line variety of the Veronese variety, namely that its ideal is generated
by the 3x3 minors of any of the "middle" catalecticants. Part of this
conjecture is the statement that the ideals of 3x3 minors are equal for most
catalecticants, and this was known to hold set-theoretically. We prove the
equality of 3x3 minors and derive Geramita's conjecture as a consequence of
previous work by Kanev.
