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The depth of the Jacobian ring of a homogeneous polynomial in three variables

Author: Aron Simis
Journal: Proc. Amer. Math. Soc. 134 (2006), 1591-1598
MSC (2000): Primary 13C14, 13C15, 13H10, 13D02, 13D40, 13H15; Secondary 12E05, 14B05, 14H50
Published electronically: December 2, 2005
MathSciNet review: 2204268
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Abstract | References | Similar Articles | Additional Information

Abstract: The question as to whether the Jacobian ideal of an irreducible projective plane curve always admits an irrelevant component has been going around for some years. One shows that a curve will satisfy this if it has only ordinary nodes or cusps, while an example is given of a family of sextic curves whose respective Jacobian ideals are saturated. The connection between this problem and the theory of homogeneous free divisors in three variables is also pointed out, so the example gives a family of Koszul-free divisors.

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Additional Information

Aron Simis
Affiliation: Departamento de Matemática, CCEN, Universidade Federal de Pernambuco, Cidade Universitária, 50740-540 Recife, PE, Brazil

Received by editor(s): October 18, 2004
Received by editor(s) in revised form: January 6, 2005
Published electronically: December 2, 2005
Additional Notes: The author was partially supported by a CNPq grant and the Brazil–France Cooperation in Mathematics.
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.