Student CA Seminar: Introduction to liaison theory

Roughly speaking, two projective varieties of the same dimension are geometrically linked if they have no components in common and their union is a complete intersection. On the algebraic side, ideals I and J are linked if we can find a regular sequence x_1, ..., x_n with J = (x_1, ..., x_n) : I and I = (x_1, ..., x_n) : J. We will take a look at what properties are (and are not) preserved by linkage, as well as looking at a commonly-studied equivalence class of linked ideals.