The Waring loci of ternary quartics.
On the invariant theory of the Bézoutiant.
Decomposable ternary cubics.
On the Jacobian ideal of the binary discriminant.
Let Δ denote the discriminant of the generic binary -ic. We show that for d ≥ 3, the Jacobian ideal of Δ is perfect of height 2. Moreover we describe its SL-equivariant minimal resolution and the associated differential equations satisfied by Δ. A similar result is proved for the resultant of two forms of orders , whenever ≥ -1. If Φ denotes the locus of binary forms with total root multiplicity ≥ -n, then we show that the ideal of Φ is also perfect, and we construct a covariant which characterizes...
The higher transvectants are redundant
Let denote generic binary forms, and let denote their -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the . As a consequence, we show that each of the higher transvectants is redundant in the sense that it can be completely recovered from and . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of -representations, and the...
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