Related papers: Jet schemes and singularities

We present two versions of third order accurate jet schemes, which achieve high order accuracy by tracking derivative information of the solution along characteristic curves. For a benchmark linear advection problem, the efficiency of jet…

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…

This talk reviews some key developments that have taken place in hadron-collider jet finding over the past couple of years, including: technical advances such as the complete formulation of an infrared safe seedless cone algorithm and fast…

We prove that every smooth subelliptic variety admits a surjective morphism from an affine space. This result gives partial answers to the questions of Arzhantsev and Forstneri\v{c}. As an application, we characterize open images of…

We study singularities obtained by the contraction of the maximal divisor in compact (non kaehlerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be Q-Gorenstein, numerically Gorenstein or…

We introduce a class of singular log schemes in three dimensions and conjecture that log schemes in this class admit log crepant log resolutions. We provide examples as evidence and relate this conjecture to the conjecture made in [4] and…

This article studies jet schemes of monomial schemes. They are known to be equidimensional but usually are not reduced. We thus investigate their structure further, giving a formula for the multiplicity along every component of the jet…

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…

In this paper we study singularities defined by the action of Frobenius in characteristic $p > 0$. We prove results analogous to inversion of adjunction along a center of log canonicity. For example, we show that if $X$ is a Gorenstein…

A short explanation of the complexity of the structure of Demailly-semple invariant jet differentials was given

Using the rudiments of pde jets theory in a nonstandard setting, we first deepen and extend previous nonstandard existence results for generalized solutions of linear differential equations and second extend the previous results for linear…

We establish Thom's jet transversality theorem for regular maps from an affine algebraic manifold to an algebraic manifold satisfying a suitable flexibility condition. It can be considered as the algebraic version of Forstneri\v{c}'s jet…

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 compute the minimal log discrepancies of determinantal varieties of square matrices, and more generally of pairs $\bigl(D^k,\sum \alpha_i D^{k_i}\bigr)$ consisting of a determinantal variety (of square matrices) and an $\mathbb R$-linear…

We show that for a complete complex algebraic variety the pure component of homology coincides with the image of intersection homology. Therefore pure homology is topologically invariant. To obtain slightly more general results we introduce…

We generalize the Guth--Katz joints theorem from lines to varieties. A special case says that $N$ planes (2-flats) in 6 dimensions (over any field) have $O(N^{3/2})$ joints, where a joint is a point contained in a triple of these planes not…

In this paper we generalize the definitions of singularities of pairs and multiplier ideal sheaves to pairs on arbitrary normal varieties, without any assumption on the variety being Q-Gorenstein or the pair being log Q-Gorenstein. The main…

Consider a smooth projective curve and a given embedding into projective space via a sufficiently positive line bundle. We can form the secant variety of $k$-planes through the curve. These are singular varieties, with each secant variety…

In this article we explore some of the combinatorial consequences of recent results relating the isospectral commuting variety and the Hilbert scheme of points in the plane.

Jet substructure is typically studied using clustering algorithms, such as kT, which arrange the jets' constituents into trees. Instead of considering a single tree per jet, we propose that multiple trees should be considered, weighted by…