Related papers: Jets via Hasse-Schmidt Derivations
These notes are an exposition and synthesis of various "jet space" constructions in complex analytic geometry. They are written primarily for model-theorists interested in the results of Campana and Fujiki (whose model-theoretic…
We extend Borger's construction of algebraic jet spaces to allow for an arbitrary prolongation sequence, clarify the relation between Borger's and Buium's jet spaces and compare them in the extended sense. As a result, we strengthen a…
We give explicit estimates for the volume of the Green-Griffiths jet differentials of any order on a toroidal compactification of a ball quotient. To this end, we first determine the growth of the logarithmic Green-Griffiths jet…
Outstanding questions in the study of relativistic jets in their various astrophysical settings are discussed in the context of a general dynamical model.
Jets are an important probe to identify the hard interaction of interest at the LHC. They are routinely used in Standard Model precision measurements as well as in searches for new heavy particles, including jet substructure methods. In…
This paper concerns the model theory of jet spaces (i.e., higher-order tangent spaces) in differentially closed fields. Suppose p is the generic type of the jet space to a finite dimensional differential-algebraic variety at a generic…
We develop the theory of higher prolongations of algebraic varieties over fields in arbitrary characteristic with commuting Hasse-Schmidt derivations. Prolongations were introduced by Buium in the context of fields of characteristic 0 with…
We introduce the concept of the area of a jet, and show how it can be used to perform the subtraction of even a large amount of diffuse noise from hard jets.
This paper is the sequel to our previous paper (Differetial Geometry of Microlinear Frolicher spaces IV-1), where three approaches to jet bundles are presented and compared. The first objective in this paper is to give the affine bundle…
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…
The paper considers the formulation of higher-order continuum mechanics on differentiable manifolds devoid of any metric or parallelism structure. For generalized velocities modeled as sections of some vector bundle, a variational kth order…
Systems of partial differential equations lie at the heart of physics. Despite this, the general theory of these systems has remained rather obscure in comparison to numerical approaches such as finite element models and various other…
Image-based jet analysis is built upon the jet image representation of jets that enables a direct connection between high energy physics and the fields of computer vision and deep learning. Through this connection, a wide array of new jet…
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 discuss the de Rham cohomology of some…
This is an account of the algebraic geometry of Witt vectors and arithmetic jet spaces. The usual, "p-typical" Witt vectors of p-adic schemes of finite type are already reasonably well understood. The main point here is to generalize this…
Jet manifolds and vector bundles allow one to employ tools of differential geometry to study differential equations, for example those arising as equations of motions in physics. They are necessary for a geometrical formulation of…
The phenomenology of jets associated with a variety of black hole systems is summarized, emphasizing the constraints imposed on their origin. Models of jet formation are reviewed, focusing in particular on recent ideas concerning MHD…
We provide detailed holomorphic Morse estimates for the cohomology of sheaves of jet differentials and their dual sheaves. These estimates apply on arbitrary directed varieties, and a special attention has been given to the analysis of the…
We define and study jet bundles in the geometric orbifold category. We show that the usual arguments from the compact and the logarithmic settings do not all extend to this more general framework. This is illustrated by simple examples of…
In this paper, we collect the fundamental basic properties of jet modules in algebraic geometry and related properties of differential operators. We claim no originality but we want to provide a reference work for own research and the…