Related papers: Differentials on the arc space
The space of the global sections of chiral de Rham complex on a compact Ricci-flat K\"ahler manifold is calculated and it is expressed as an invariant subspace of a $\beta\gamma-bc$ system under the action of certain Lie algebra.
A reduced divisor on a nonsingular variety defines the sheaf of logarithmic 1-forms. We introduce a certain coherent sheaf whose double dual coincides with this sheaf. It has some nice properties, for example, the residue exact sequence…
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…
Sheaf cohomology or, more generally, higher direct images of coherent sheaves along proper morphisms are central to modern algebraic geometry. However, the computation of these objects is a non-trivial and expensive task which easily…
We describe derived moduli functors for a range of problems involving schemes and quasi-coherent sheaves, and give cohomological conditions for them to be representable by derived geometric n-stacks. Examples of problems represented by…
We consider a shear layer of a kind not previously studied to our knowledge. Contrary to the classical free shear layer, the width of the shear zone does not vary in the streamwise direction but rather exhibits a lateral variation. Based on…
The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on…
We discuss hypercomplex and hyperk\"ahler structures obtained from higher degree curves in complex spaces fibring over ${\mathbb{P}}^1$.
In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus. From our investigation, we can derive many interesting identities of several polynomials
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…
We define and study jets of flat partial connections in the setting of smooth foliations and flat partial connections on locally free sheaves. In the case of codimension one foliations, we apply this definition to characterize transversely…
We study the space of arcs on a singularity of the form xy=f(z_1,..., z_n) and prove 2 main results. (i) The number of irreducible components equals the multiplicity of f minus 1. (ii) If n>1 and the leading homogeneous term of f is not a…
Let $k$ be a field, $C\to \Spec k$ be a stable curve and let $G$ be a finite group acting faithfully on the curve $C\to \Spec k$. In this article, we compute the vector space $\Ext^1_G(\Omega_{C/k}, \O_C)$, the sheaf $\Omega_{C/k}$ being…
We introduce moduli spaces of flags of sheaves on P^2, and use them to obtain functors between the derived categories of the usual moduli spaces of sheaves on P^2. These functors induce an action of the shuffle algebra on K-theory, by…
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…
We develop a generalized field space geometry for higher-derivative scalar field theories, expressing scattering amplitudes in terms of a covariant geometry on the all-order jet bundle. The incorporation of spacetime and field derivative…
It is known that the vector space spanned by labeled rooted trees forms a Hopf algebra. Let k be a field and let R be a commutative k-algebra. Let H denote the Hopf algebra of rooted trees labeled using derivations D in Der(R). In this…
We give a self-dual t-structure on the derived category of $\mathbb{R}$-constructible sheaves over a Noetherian regular ring by generalizing the notion of t-structure.
We establish a version of Kashiwara's theorem for twisted sheaves of Berthelot's arithmetic differential operators for a closed immersion between smooth p-adic formal schemes. As an application, we construct simple modules for crystalline…
We study the homotopy theory of locally ordered spaces, that is manifolds with boundary whose charts are partially ordered in a compatible way. Their category is not particularly well-behaved with respect to colimits. However, this category…