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On the Jacobian ideal of the binary discriminant

Carlos D'Andrea·Jaydeep Chipalkatti·Abdelmalek Abdesselam
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Abstract

Let $Δ$ denote the discriminant of a generic binary $d$-ic. We show that for $d \ge 3$, the Jacobian ideal of $Δ$ is perfect of height 2. Moreover, we describe its SL_2-equivariant minimal resolution, and the associated invariant differential equations satisfied by $Δ$. A similar result is proved for the resultant of two forms of orders $d,e$, whenever $d \ge e-1$. 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.

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Carlos D'Andrea, Jaydeep Chipalkatti, Abdelmalek Abdesselam. 2006-01-29. On the Jacobian ideal of the binary discriminant. https://arxiv.org/abs/math/0601705

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