Related papers: Geometric properties of jet schemes

In this review the foundations of Geometric Quantization are explained and discussed. In particular, we want to clarify the mathematical aspects related to the geometrical structures involved in this theory: complex line bundles, hermitian…

We establish the finiteness of periodic points, that we called Geometric Dynamical Northcott Property, for regular polynomials automorphisms of the affine plane over a function field $\mathbf{K}$ of characteristic zero, improving results of…

A brief exposition of the general theory of characteristic classes of quantum principal bundles is given. The theory of quantum characteristic classes incorporates ideas of classical Weil theory into the conceptual framework of…

In this paper, we prove a similar result to the fundamental theorem of regular surfaces in classical differential geometry, which extends the classical theorem to the entire class of singular surfaces in Euclidean 3-space known as frontals.…

In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…

In the jet bundle description of Field Theories (multisymplectic models, in particular), there are several choices for the multimomentum bundle where the covariant Hamiltonian formalism takes place. As a consequence, several proposals for…

Let S be a Noetherian scheme, f:X->Y a surjective S-morphism of S-schemes, with X of finite type over S. We discuss what makes Y of finite type. First, we prove that if S is excellent, Y is reduced, and f is universally open, then Y is of…

This paper is concerned with basic geometric properties of the phase space of a classical general relativistic particle, regarded as the 1st jet space of motions, i.e. as the 1st jet space of timelike 1--dimensional submanifolds of…

Congruences, or $2$-parameter families of lines in $3$-space are of interest in many situations, in particular in geometric optics. In this paper we consider elements of their geometry which are invariant under affine changes of…

We study the singularities of the moduli space of degree $e$ maps from smooth genus $g$ curves to an arbitrary smooth hypersurface of low degree. For $e$ large compared to $g$, we show that these moduli spaces have at worst terminal…

In anabelian geometry, we consider to what extent the \'{e}tale or tame fundamental groups of schemes reflect geometric properties of the schemes. Although there are many known results (mainly for smooth curves) in this area, general…

These Lectures summarize the relevant material on existent applications of jet manifold techniques to classical and quantum field theory. The following topics are included: 1. Fibre bundles, 2. Jet manifolds, 3. Connections, 4. Lagrangian…

Many analyses at the collider utilize the hadronic jets that are the footprints of QCD partons. These are used both to study the QCD processes themselves and increasingly as tools to study other physics, for example top mass reconstruction.…

Two significant directions in the development of jet calculus are showed. First, jets are generalized to so-called quasijets. Second, jets of foliated and multifoliate manifold morphisms are presented. Although the paper has mainly a survey…

We present our studies on jet-induced modifications of the characteristic of the bulk nuclear matter. To describe such a matter, we use efficient relativistic hydrodynamic simulations in (3+1) dimensions employing the Graphics Processing…

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 study jet schemes and arc spaces in the context of derived algebraic geometry. Explicitly, we consider the jet and arc functors in the category of schemes and study their animations to the category of derived schemes -- what we call the…

The study of the differences of the fragmentation of quarks and gluons to jets of hadrons gives insight into the fundamental structure of QCD. Results from different approaches to properties of quarks and gluons are shown. The colour factor…

In this paper, we show how information geometry, the natural geometry of discrete probability distributions, can be used to derive the quantum formalism. The derivation rests upon three elementary features of quantum phenomena, namely…

We study the holomorphic Euler characteristics of tautological sheaves on Hilbert schemes of points on surfaces. In particular, we establish the rationality of K-theoretic descendent series. Our approach is to control equivariant…