Let Δ denote the discriminant of the generic binary d-ic. We show that for d ≥ 3, the Jacobian ideal of Δ is perfect of height 2. Moreover we describe its SL2-equivariant minimal resolution and the associated differential equations satisfied by Δ. A similar result is proved for the resultant of two forms of orders d, e whenever d ≥ e-1. If Φn denotes the locus of binary forms with total root multiplicity ≥ d-n, then we show that the ideal of Φn is also perfect, and we construct a covariant which characterizes this locus. We also explain the role of the Morley form in the determinantal formula for the resultant. This relies upon a calculation which is done in the appendix by A. Abdesselam.
@article{urn:eudml:doc:41803,
title = {On the Jacobian ideal of the binary discriminant.},
journal = {Collectanea Mathematica},
volume = {58},
year = {2007},
pages = {155-180},
zbl = {1124.13002},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41803}
}
D'Andrea, Carlos; Chipalkatti, Jaydeep. On the Jacobian ideal of the binary discriminant.. Collectanea Mathematica, Tome 58 (2007) pp. 155-180. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41803/