# On the Jacobian ideal of the binary discriminant.

Carlos D'Andrea; Jaydeep Chipalkatti

Collectanea Mathematica (2007)

- Volume: 58, Issue: 1, page 155-180
- ISSN: 0010-0757

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topD'Andrea, Carlos, and Chipalkatti, Jaydeep. "On the Jacobian ideal of the binary discriminant.." Collectanea Mathematica 58.1 (2007): 155-180. <http://eudml.org/doc/41803>.

@article{DAndrea2007,

abstract = {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.},

author = {D'Andrea, Carlos, Chipalkatti, Jaydeep},

journal = {Collectanea Mathematica},

keywords = {Anillos conmutativos; Invariantes; Ideales},

language = {eng},

number = {1},

pages = {155-180},

title = {On the Jacobian ideal of the binary discriminant.},

url = {http://eudml.org/doc/41803},

volume = {58},

year = {2007},

}

TY - JOUR

AU - D'Andrea, Carlos

AU - Chipalkatti, Jaydeep

TI - On the Jacobian ideal of the binary discriminant.

JO - Collectanea Mathematica

PY - 2007

VL - 58

IS - 1

SP - 155

EP - 180

AB - 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.

LA - eng

KW - Anillos conmutativos; Invariantes; Ideales

UR - http://eudml.org/doc/41803

ER -