The dimension of jet schemes of singular varieties

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.

arXiv comment22 pages, to appear in the Proceedings of the ICM, Seoul 2014

References in corpus (3)

• Arcs on Determinantal Varieties
• Log canonical thresholds in positive characteristic
• Jet schemes of homogeneous hypersurfaces

Cited by in corpus (2)

• Computations of Mather Minimal Log Discrepancies
• Arc closures and the local isomorphism problem