A case study in bigraded commutative algebra
Abstract
We study the commutative algebra of three bihomogeneous polynomials p0,p1,p2 of degree (2,1) in variables x,y;z,w, assuming that they never vanish simultaneously on P1 x P1. Unlike the situation for P2, the Koszul complex of the pi is never exact. The purpose of this article is to illustrate how bigraded commutative algebra differs from the classical graded case and to indicate some of the theoretical tools needed to understand the free resolution of the ideal generated by p0,p1,p2.
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