Related papers: Contact loci in arc spaces
We give an elementary construction of symplectic connections through reduction. This provides an elegant description of a class of symmetric spaces and gives examples of symplectic connections with Ricci type curvature, which are not…
Our start point is a 3D piecewise smooth vector field defined in two zones and presenting a shared fold curve for the two smooth vector fields considered. Moreover, these smooth vector fields are symmetric relative to the fold curve, giving…
Over fields of characteristic zero, we determine all absolutely irreducible Yetter-Drinfeld modules over groups that have prime dimension and yield a finite-dimensional Nichols algebra. To achieve our goal, we introduce orders of braided…
We continue the study of linear families of contact forms on 3-manifolds begun in our paper `Contact geometry and complex surfaces'. The present paper introduces Teichmuller and moduli spaces for so-called taut contact circles. By…
In this work we characterize the subsets of ${\mathbb R}^n$ that are images of Nash maps $f:{\mathbb R}^m\to{\mathbb R}^n$. We prove Shiota's conjecture and show that a subset ${\mathcal S}\subset{\mathbb R}^n$ is the image of a Nash map…
We investigate the definability (reducts) lattice of the order of integers and describe a sublattice generated by relations 'between', 'cycle', 'separation', 'neighbor', '1-codirection', 'order' and equality'. Some open questions are…
A topological space $X$ is called resolvable if it contains a dense subset with dense complement. Using only basic principles, we show that whenever the space $X$ has a resolving subset that can be written as an at most countably infinite…
We shall prove that a moduli space of flat irreducible Lie algebroid connections over a compact manifold has locally a natural structure of a smooth differentiable space. This is a generalization of some well known results for the moduli…
We prove that the category of vector bundles over a fixed smooth manifold and its corresponding category of convenient modules are models for intuitionistic differential linear logic. The exponential modality is modelled by composing the…
We establish a local model for the moduli space of holomorphic symplectic structures with logarithmic poles, near the locus of structures whose polar divisor is normal crossings. In contrast to the case without poles, the moduli space is…
The tensor powers of the vector representation associated to an infinite rank quantum group decompose into irreducible components with multiplicities independant of the infinite root system considered. Although the irreducible modules…
Given a finite unbranched covering of a nonsingular projective scheme we analyse the morphism between moduli spaces of sheaves induced by pullback. We have a closer look at cyclic coverings and, in particular, at canonical coverings of…
This paper is an introduction to the jet schemes and the arc space of an algebraic variety. We also introduce the Nash problem on arc families.
This paper introduces an infinite linear hierarchy for the homogeneous, incompressible three-dimensional Navier-Stokes equation. The Cauchy problem of the hierarchy with a factorized divergence-free initial datum is shown to be equivalent…
Motivated by applications to vortex rings, we study the Cauchy problem for the three-dimensional axisymmetric Navier-Stokes equations without swirl, using scale invariant function spaces. If the axisymmetric vorticity is integrable with…
A few basic, intuitive, properties of the Navier-Stokes system of equations for incompressible fluid flows are discussed in this paper. We present a rephrased interpretation of the Navier-Stokes equation in a space having an arbitrary…
We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem…
Some moduli spaces of irregular connections on the trivial bundle over the Riemann sphere will be identified with Nakajima quiver varieties. In particular this enables us to associate a Kac-Moody root system to such connections (yielding…
We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Euclidean distance degree, which pertains to first-order…
We study moduli of semistable twisted sheaves on smooth proper morphisms of algebraic spaces. In the case of a relative curve or surface, we prove results on the structure of these spaces. For curves, they are essentially isomorphic to…