# Jets via Hasse-Schmidt Derivations

@article{Vojta2004JetsVH, title={Jets via Hasse-Schmidt Derivations}, author={Paul Vojta}, journal={arXiv: Algebraic Geometry}, year={2004} }

This note is intended to provide a general reference for jet spaces and jet differentials, valid in maximal generality (at the level of EGA). The approach is rather concrete, using Hasse-Schmidt (divided) higher differentials. Discussion of projectivized jet spaces (as in Green and Griffiths (1980)) is included.

## 36 Citations

### Smoothness and jet schemes

- Mathematics
- 2008

This paper shows some criteria for a scheme of finite type over an algebraically closed field to be non-singular in terms of jet schemes.
For the base field of characteristic zero, the scheme is…

### Differentials on the arc space

- MathematicsDuke Mathematical Journal
- 2020

The paper provides a description of the sheaves of Kahler differentials of the arc space and jet schemes of an arbitrary scheme where these sheaves are computed directly from the sheaf of…

### Higher Derivations of Modules and the Hasse–Schmidt Module

- MathematicsMichigan Mathematical Journal
- 2022

In this paper we revisit Ribenboim's notion of higher derivations of modules and relate it to the recent work of De Fernex and Docampo on the sheaf of differentials of the arc space. In particular,…

### Jet schemes and minimal embedded desingularization of plane branches

- Mathematics
- 2013

For a plane branch C with g Puiseux pairs, we determine the irreducible components of its jet schemes which correspond to the star (or rupture) and end divisors that appear on the dual graph of the…

### Differential forms on arithmetic jet spaces

- Mathematics
- 2009

We study derivations and differential forms on the arithmetic jet spaces of smooth schemes, relative to several primes. As applications, we give a new interpretation of arithmetic Laplacians, and we…

### DEFORMING SPACES OF M-JETS OF ISOLATED HYPERSURFACES SINGULARITIES

- Mathematics
- 2015

Deformation of Spaces of m-jets. Let K be an algebraically closed field of characteristic zero, and V a hypersurface defined by an irreducible polynomial f with coefficents in K. We suppose that V…

### Jet schemes of rational double point singularities

- Mathematics
- 2013

We prove that for m ∈ N, m big enough, the number of irreducible components of the schemes of m−jets centered at a point which is a double point singularity is independent of m and is equal to the…

### Arc spaces and the Rogers–Ramanujan identities

- Mathematics
- 2011

Arc spaces have been introduced in algebraic geometry as a tool to study singularities but they show strong connections with combinatorics as well. Exploiting these relations, we obtain a new…

### Arcs on determinantal varieties

- Mathematics
- 2012

We study arc spaces and jet schemes of generic determinantal varieties. Using the natural group action, we decompose the arc spaces into orbits, and analyze their structure. This allows us to compute…

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