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Title: On the Jacobian ideal of the binary discriminant (with an appendix by Abdelmalek Abdesselam)
Author: D'Andrea, Carlos, 1973-
Chipalkatti, Jaydeep
Keywords: Geometria algebraica
Algebraic geometry
Issue Date: 2007
Publisher: Universitat de Barcelona
Abstract: Let ∆ denote the discriminant of the generic binary d-ic. We show that for d ≥ 3, the Jacobian ideal of ∆ is perfect of height 2. Moreover we describe its SL2-equivariant 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 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.
Note: Reproducció del document publicat a:
It is part of: Collectanea Mathematica, 2007, vol. 58, num. 2, p. 155-180
ISSN: 0010-0757
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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