Algebra Seminar - Groebner basis of ideals of points in P^1 x P^1 ", Jason Palombaro"
Title: Groebner basis of ideals of points in P^1 x P^1
Abstract: There are two new results on the Groebner bases of defining ideals of finite sets of points in P^1 x P^1 that will be presented. The first new result is the Universal Groebner basis for an Arithmetically Cohen-Macaulay set of points in P^1 x P^1. Following that, we will look at the Buchberger-Moeller algorithm and see how it can be modified to compute the reduced Groebner basis for the defining ideal of any finite set of points in P^1 x P^1. We end with a short example to show how the new algorithm works.