On the Jacobian ring of a complete intersection

Details On the Jacobian ring of a complete intersection On the Jacobian ring of a complete intersection

2006-10-06

arxiv.org/abs/math/0610228v1

Mathematics

Algebraic Geometry

28 pages, no figures

Scientific paper

Let f_1,...,f_r be homogeneous polynomials in K[x_1,...,x_n], K a field. Put
F=y_1f_1+...+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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