Algebra & Number Theory Seminar | Department Home
Texas Tech University
Title: An Ideal Solitude Puzzle
Abstract:
The common solutions to a system of polynomial equations in three variables define an algebraic variety in 3-dimensional space. Two such varieties are said to be linked if their union is a particularly nice kind of variety. Thus, linked varieties are in some sense complementary: one carries an imprint of the other.
Linkage has an algebraic incarnation that is used to study ideals. In the talk I will discuss how the idea that linked ideals are "complementary" can be used to unwind the detailed structure of a classification of ideals in the ring of polynomials in three variables. What that structure is only became clear to us---Oana Veliche, Jerzy Weyman, and myself---after extensive experimentation, and justifying it rigorously felt, at times, like solving a solitaire.