Related papers: Jet schemes, arc spaces and the Nash problem

We give an answer in the "geometric" setting to a question of de Fernex, Ein, and Ishii, asking when local isomorphisms of $k$-schemes can be detected on the associated maps of local arc or jet schemes. In particular, we show that their…

We consider in this paper the $FRS$-deformations of a family of space curves with codimension $\leq 3$. Some geometric aspects of a space curve such as flattenings, vertices and twistings points has been studied.

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.…

The study of the internal structure of hadronic jets has become in recent years a very active area of research in particle physics. Jet substructure techniques are increasingly used in experimental analyses by the LHC collaborations, both…

We introduce perfect resolving algebras and study their fundamental properties. These algebras are basic for our theory of differential graded schemes, as they give rise to affine differential graded schemes. We also introduce etale…

We introduce new notions of log jet spaces. Mildly singular spaces are ``smooth'' in log geometry, so their log jet spaces behave like the jet spaces of smooth varieties. Myriad examples contrast log jet spaces with the usual jet spaces of…

We introduce a geometric construction which relates to the pentagram map much in the way that a logarithmic spiral relates to a circle. After introducing the construction, we establish some basic geometric facts about it, and speculate on…

The significance of jets and accretion disks in Astrophysics may be growing far beyond any single example of recent finds in the scientific journals. This brief review will summarize recent, significant manifestations of accretion disk…

Plane arrangements are a useful tool for surface and volume modelling. However, their main drawback is poor scalability. We introduce two key novelties that enable the construction of plane arrangements for complex objects and entire…

Let $k$ be an algebraically closed field, $S$ a variety over $k$ and m a nonnegative integer. There is a space $S_m$ over $S$ , called the jet scheme of $X$ of order $m$, parameterizing $m$-th jets on $S$. The fiber over the singular locus…

This paper describes our attempt to understand the recent success of Na Wang in constructing the 3-Schur polynomials, associated with the plane partitions. We provide a rather detailed review and try to figure out the new insights, which…

This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…

We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied.

We identify and study a matrix algebra consisting of Pascal-type matrices. The generator of the matrix algebra is shown to well define a canonical bundle map, called the Pascal map on jet bundles, and we use it to give an intrinsic…

We study the relative Hilbert scheme of a family of nodal (or smooth) curves via its (birational) cycle map, going to the relative symmetric product. We show the cycle map is the blowing up of the discriminant locus, which consists of…

The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…

The Hilbert scheme $S^{[n]}$ of points on an algebraic surface $S$ is a simple example of a moduli space and also a nice (crepant) resolution of singularities of the symmetric power $S^{(n)}$. For many phenomena expected for moduli spaces…

The purpose of this article is to introduce projective geometry over composition algebras : the equivalent of projective spaces and Grassmannians over them are defined. It will follow from this definition that the projective spaces are in…

This is an elementary exposition of the basic descent theorems for algebraic schemes over fields (Grothendieck, Weil, ...).

We give a definition of associative schemes, schemes of associative rings, over a field $k,$ using the definition of completion of an associative $k$-algebra in a finite set of simple modules. We start by giving a weaker but sufficient…