相关论文: Multiplier Ideals, V-filtrations and Transversal S…
In this paper, we give formulas for $v$-number of edge ideals of some graphs like path, cycle, 1-clique sum of a path and a cycle, 1-clique sum of two cycles and join of two graphs. For an $\mathfrak{m}$-primary monomial ideal $I\subset…
Earlier the authors considered and, in some cases, computed Poincare series of two sorts of multi-index filtrations on the ring of germs of functions on a complex (normal) surface singularity (in particular on the complex plane). A…
The purpose of this paper is to show that the multiplicities of a discrete series representation relatively to a compact subgroup can be "computed" geometrically, in the way predicted by the "qantization commutes with reduction" principle…
In this paper, we study the algebra of Veronese type. We show that the presentation ideal of this algebra has an initial ideal whose Alexander dual has linear quotients. As an application, we explicitly obtain the Castelnuovo-Mumford…
We provide a description of Voevodsky's $\infty$-category of motivic spectra in terms of the subcategory of motives of smooth proper varieties. As applications, we construct weight filtrations on the Betti and \'{e}tale cohomologies of…
An analogue of the Stefan-Sussmann Theorem on manifolds with boundary is proven for normal distributions. These distributions contain vectors transverse to the boundary along its entirety. Plain integral manifolds are not enough to…
We consider the multiplier ideals of the ideal of a reduced union of lines through the origin in C^3. For general arrangements of lines, we calculate the multiplier ideals.
We consider Voevodsky's slice tower for a finite spectrum E in the motivic stable homotopy category over a perfect field k. In case k has finite cohomological dimension (in characteristic two, we also require that k is infinite), we show…
We give some new results related to the directional short-time Fourier transform (DSTFT) and extend them on the spaces $\mathcal K_{1}(\mathbb R^{n})$ and $\mathcal K_{1}({\mathbb R})\widehat{\otimes}\mathcal U(\mathbb C^n)$ and their…
This paper studies the regularity of constrained Willmore immersions into $\R^{m\ge3}$ locally around both "regular" points and around branch points, where the immersive nature of the map degenerates. We develop local asymptotic expansions…
We define a hierarchy of special classes of constrained Willmore surfaces by means of the existence of a polynomial conserved quantity of some type, filtered by an integer. Type 1 with parallel top term characterises parallel mean curvature…
We consider smooth flows preserving a smooth invariant measure, or, equivalently, locally Hamiltonian flows on compact orientable surfaces and show that almost every such locally Hamiltonian flow with only simple saddles has singular…
We present several naturally occurring classes of spectral spaces using commutative algebra on pointed monoids. For this purpose, our main tools are finite type closure operations and continuous valuations on monoids which we introduce in…
This article surveys the Weierstrass representation of surfaces in the three- and four-dimensional spaces, with an emphasis on its relation to the Willmore functional. We also describe an application of this representation to constructing a…
We propose a high-precision numerical quadrature framework based on local Fourier extension (LFE) approximations. The method constructs, on each subinterval, a truncated-SVD stabilized local Fourier continuation of the integrand on an…
We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…
Two results about equidistribution of tile orientations in primitive substitution tilings are stated, one for finitely many, one for infinitely many orientations. Furthermore, consequences for the associated diffraction spectra and the…
For any graded commutative noetherian ring, where the grading group is abelian and where commutativity is allowed to hold in a quite general sense, we establish an inclusion-preserving bijection between, on the one hand, the twist-closed…
If Com is the reduced commutative operad, the category of Com-algebras in spectra is the category of nounital commutative ring spectra. The theme of this survey is that many important constructions on Com-algebras are given by taking the…
We prove the convergence of a wide class of continued fractions, including generalized continued fractions over quaternions and octonions. Fractional points in these systems are not bounded away from the unit sphere, so that the iteration…