On the Jacobian ideal of the binary discriminant

• Autores: Carlos D'Andrea , Jaydeep V. Chipalkatti
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 58, Fasc. 2, 2007, págs. 155-180
• Idioma: inglés
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• Resumen

  • Let
    denote the discriminant of the generic binary dic.

    We show that for d  3, the Jacobian ideal of
    is perfect of height 2. Moreover we describe its SL2equivariant minimal resolution and the associated differential equations satisfied by
    . A similar result is proved for the resultant of two forms of orders d, e whenever d  e - 1. If n denotes the locus of binary forms with total root multiplicity  d-n, then we show that the ideal of n 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.

    Keywords: Discriminant, resultant, Morley form, transvectant, evectant, classical invariant theory, HilbertBurch theorem.

    MSC2000: 13A50, 13C40.

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