On the Jacobian ring of a complete intersection

Alan Adolphson; Steven Sperber

doi:10.1016/j.jalgebra.2006.06.039

On the Jacobian ring of a complete intersection

Alan Adolphson, Steven Sperber

School of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Let f₁, ..., f_r ∈ K [x], K is a field, be homogeneous polynomials and put F = ∑_{i = 1}^r y_i f_i ∈ K [x, y]. The quotient J = K [x, y] / I, where I is the ideal generated by the ∂ F / ∂ x_i and ∂ F / ∂ y_j, is the Jacobian ring of F. We describe J by computing the cohomology of a certain complex whose top cohomology group is J.

Original language	English (US)
Pages (from-to)	1193-1227
Number of pages	35
Journal	Journal of Algebra
Volume	304
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2006.06.039
State	Published - Oct 15 2006

Keywords

Complete intersection
Hodge numbers
Jacobian ring

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10.1016/j.jalgebra.2006.06.039

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abstract = "Let f1, ..., fr ∈ K [x], K is a field, be homogeneous polynomials and put F = ∑i = 1r yi fi ∈ K [x, y]. The quotient J = K [x, y] / I, where I is the ideal generated by the ∂ F / ∂ xi and ∂ F / ∂ yj, is the Jacobian ring of F. We describe J by computing the cohomology of a certain complex whose top cohomology group is J.",

keywords = "Complete intersection, Hodge numbers, Jacobian ring",

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AU - Sperber, Steven

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N2 - Let f1, ..., fr ∈ K [x], K is a field, be homogeneous polynomials and put F = ∑i = 1r yi fi ∈ K [x, y]. The quotient J = K [x, y] / I, where I is the ideal generated by the ∂ F / ∂ xi and ∂ F / ∂ yj, is the Jacobian ring of F. We describe J by computing the cohomology of a certain complex whose top cohomology group is J.

AB - Let f1, ..., fr ∈ K [x], K is a field, be homogeneous polynomials and put F = ∑i = 1r yi fi ∈ K [x, y]. The quotient J = K [x, y] / I, where I is the ideal generated by the ∂ F / ∂ xi and ∂ F / ∂ yj, is the Jacobian ring of F. We describe J by computing the cohomology of a certain complex whose top cohomology group is J.

KW - Complete intersection

KW - Hodge numbers

KW - Jacobian ring

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On the Jacobian ring of a complete intersection

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