Commutative Algebra Seminar

Title

An Ideal Solitaire Puzzle

Abstract

Two algebraic varieties are said to be linked if their union is a particularly nice kind of variety, a complete intersection. 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 explain how the idea that linked ideals are ``complementary’’ can be used to unwind the detailed structure of a classification of local rings of codimension 3. 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.