On Hermite's invariant for binary quintics

Let H⊆P5 denote the hypersurface of binary quintics in involution, with defining equation given by the Hermite invariant H. In Section 2 we find the singular locus of H, and show that it is a complete intersection of a linear covariant of quintics. In Section 3 we show that H is canonically isomorphic to its own projective dual via an involution. The Jacobian ideal of H is shown to be perfect of height two in Section 4, moreover we describe its SL2-equivariant minimal free resolution. The last section develops a general formalism for evectants of covariants of binary forms, which is then used to calculate the evectant of H.