Abstract

Moduli theory can be roughly understood as the study of classification problems. The most famous series of examples are moduli spaces of stable curves constructed by Deligne-Mumford. A lot of attention is devoted to moduli spaces of vector bundles or stable sheaves.

The most elementary example of a moduli problem is classifying points of a chosen variety This example is often cited as the most trivial example of a moduli problem and then ignored. However, in recent work, Andres F.H. and I observed that considering even this example can lead to interesting geometric constructions affecting X. I will illustrate how this moduli-theoretic treatment of X allows us to uniformly recover a lot of known disparate contraction results and give a new criterion for contracting in arbitrary dimension.