The dimension of jet schemes of singular varieties
arXiv:1404.7731
Abstract
Given a scheme X over a field k, a generalized jet scheme parametrizes maps from Spec(A) to X, where A is a finite-dimensional, local algebra over k. We give an overview of known results concerning the dimensions of these schemes when A has embedding dimension one, when they are related to invariants of singularities in birational geometry. We end with a discussion of more general jet schemes.
22 pages, to appear in the Proceedings of the ICM, Seoul 2014