Seminar

Linkage (or liaison) is an elegant theory standing on the border between
Commutative Algebra and Algebraic Geometry. Its roots go back to the
nineteenth century, although the first modern treatment appeared in 1974, in
a celebrated paper written by Peskine and Szpiro.

Since then, linkage has been an active area of research and has proved to be
a powerful tool, successfully employed in a number of circumstances, ranging
from structure theorems, to results on Hilbert scheme (smoothness,
irreducible components, etc.).

Moreover, in the last 20 years, the original theory developed two
interesting, very different, generalizations, namely, linkage by Gorenstein
ideals (or G-liaison) and residual intersection theory.

Starting from the definition of linkage, we will introduce the theory,
provide examples, discuss several results, and explain some of the main open
questions in the theories of liaison and G-liaison.