A case study in bigraded commutative algebra

Details A case study in bigraded commutative algebra A case study in bigraded commutative algebra

2004-09-23

arxiv.org/abs/math/0409462v2

Lecture notes in Pure and Applied Mathematics 254, (2007), 67--112

Mathematics

Commutative Algebra

36 pages. Connections with existing literature and to the implicitization problem in geometric modeling are stressed

Scientific paper

We study the commutative algebra of three bihomogeneous polynomials p_0,p_1,p_2 of degree (2,1) in variables x,y;z,w, assuming that they never vanish simultaneously on P^1 x P^1. Unlike the situation for P^2, the Koszul complex of the p_i 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 p_0,p_1,p_2.

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