相关论文: On jet closures of singularities
The question of finding solutions to given implicit differential equations (IDE) has been answered by several authors in the last few years, using different approaches, in an algebraic and also a geometric setting. Many of those results…
This paper has two main goals. First, we give a complete, explicit, and computable solution to the problem of when two simple closed curves on a surface are equivalent under the Johnson kernel. Second, we show that the Johnson filtration…
Given a feature set for the shape of a closed loop, it is natural to ask which features in that set do not change when the starting point of the path is moved. For example, in two dimensions, the area enclosed by the path does not depend on…
We introduce persistent Betti numbers to characterize topological structure of jets. These topological invariants measure multiplicity and connectivity of jet branches at a given scale threshold, while their persistence records evolution of…
Given a closed subscheme $Z$ of a polarized abelian variety $(A,\ell)$ we define its vanishing threshold with respect to $\ell$ and relate it to the Seshadri constant of the ideal defining $Z.$ As a particular case, we introduce the notion…
The purpose of this paper is to study finiteness conditions on injective hulls of simple modules over Noetherian Down-Up algebras. We will show that the Noetherian Down-Up algebras A(\alpha,\beta,\gamma) which are fully bounded are…
We prove that two arbitrary ideals $I \subset J$ in an equidimensional and universally catenary Noetherian local ring have the same integral closure if and only if they have the same multiplicity sequence. We also obtain a Principle of…
This work presents a predictive two-point statistical closure framework for turbulence formulated in physical space. A closure model for ensemble-averaged, incompressible homogeneous isotropic turbulence (HIT) is developed as a starting…
The integrability problem for transitive Lie algebroids can be looked at from different perspectives, revealing an interplay between cohomological methods and homotopical constructions. Mackenzie introduced a cohomological obstruction…
In the present paper we set up a connection between the indices of the Tits algebras of a simple linear algebraic group $G$ and the degree one parameters of its motivic $J$-invariant. Our main technical tool are the second Chern class map…
We introduce a notion of a homological index of a holomorphic 1-form on a germ of a complex analytic variety with an isolated singularity, inspired by X. G\'omez-Mont and G.-M. Greuel. For isolated complete intersection singularities it…
We exhibit a family of graphs that develop turning singularities (i.e. their Lipschitz seminorm blows up and they cease to be a graph, passing from the stable to the unstable regime) for the inhomogeneous, two-phase Muskat problem where the…
This paper deals with the characterization, in terms of closedness of certain sets regarding other sets, of Farkas lemmas determining when the upperlevel set of a given convex function contains the intersection, say F, of a convex set of a…
We construct a local invariant for resolution of singularities of 2-dimensional excellent Noetherian schemes with boundary. We prove that the invariant strictly decreases at every step of the algorithm of Cossart, Jannsen and Saito.
The aims of this work are to study Rees algebras of filtrations of monomial ideals associated to covering polyhedra of rational matrices with non-negative entries and non-zero columns using combinatorial optimization and integer…
We derive a singular version of the Sphere Covering Inequality which was recently introduced in [42], suitable for treating singular Liouville-type problems with superharmonic weights. As an application we deduce new uniqueness results for…
We study computational aspects of the tight closure of a homogeneous primary ideal in a two-dimensional normal standard-graded domain. We show how to use slope criteria for the sheaf of syzygies for generators of the ideal to compute the…
Over a field of characteristic zero, every deformation problem with cohomology constraints is controlled by a pair consisting of a differential graded Lie algebra together with a module. Unfortunately, these pairs are usually…
Closure operations such as tight and integral closure and test ideals have appeared frequently in the study of commutative algebra. This articles serves as a survey of the authors' prior results connecting closure operations, test ideals,…
Let $\fg$ be a simple finite-dimensional complex Lie algebra with a Cartan subalgebra $\fh$ and Weyl group $W$. Let $\fg_n$ denote the Lie algebra of $n$-jets on $\fg$. A theorem of Rais and Tauvel and Geoffriau identifies the centre of the…