On the Jacobian ring of a complete intersection

2006/10/06 by Alan Adolphson, Steven Sperber, Adolphson, Alan +1 · 1 citation
Mathematics · #13D25 #14F40 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #math.AG #msc:13D25 #msc:14F40

paper · pdf · doi:10.48550/arxiv.math/0610228

28 pages, no figures

arxiv created 2006/10/06 · openalex publication_date 2006/10/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f₁,...,f_r be homogeneous polynomials in K[x₁,...,x_n], K a field. Put F=y₁f₁+...+y_rf_r in K[x,y] and let I be the ideal of K[x,y] generated by the partials of F relative to the x_i and y_j. The Jacobian ring of F is the quotient J:=K[x,y]/I. We describe J by computing the cohomology of a certain complex whose top cohomology group is J.

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