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On the Jacobian ideal of the binary discriminant.

Carlos D'Andrea;  Jaydeep Chipalkatti — 2007

Collectanea Mathematica

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

Abdelmalek Abdesselam;  Jaydeep Chipalkatti — 2009

Annales de l’institut Fourier

Let A , B denote generic binary forms, and let 𝔲 r = ( A , B ) r denote their r -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the { 𝔲 r } . As a consequence, we show that each of the higher transvectants { 𝔲 r : r ≥ 2 } is redundant in the sense that it can be completely recovered from 𝔲 0 and 𝔲 1 . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of S L 2 -representations, and the...

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