# 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.

## 48 Citations

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…

JET SCHEMES, ARC SPACES AND THE NASH PROBLEM

- Mathematics
- 2007

This paper is an introduction to the jet schemes and the arc space of an algebraic variety. We also introduce the Nash problem on arc families. Resume. Ce papier constitue une introduction aux…

Logarithmic jet spaces and intersection multiplicities

- Mathematics
- 2009

The theory of relative logarithmic jet spaces is developed for log schemes. With this theory the existence of bounds of intersection multiplicities of curves and divisors on certain log schemes is…

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…

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© Publications mathématiques de l’I.H.É.S., 1969, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://…