On the Jacobian ideal of the binary discriminant.

D'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 -