Related papers: Functoriality in resolution of singularities

In this paper, using the similarity method, we construct particular solutions with singularities for degenerate high-order equations. The considered equations have singularities of the first and second kind. Particular solutions are…

In characteristic zero, we construct a canonical, functorial resolution algorithm by weighted blow-ups that strictly preserves the normal crossings (nc) locus, effectively answering Kollar's problem. Operating in full generality, our…

In this article we present a parallel modular algorithm to compute all solutions with multiplicities of a given zero-dimensional polynomial system of equations over the rationals. In fact, we compute a triangular decomposition using…

The main aim of this paper is to characterize ideals I in the power series ring R=K[[x1,...,xs]] that are finitely determined up to contact equivalence by proving that this is the case if and only if I is an isolated complete intersection…

By introducing a new classification of the growth rate of exponential functions, singular solutions for semilinear elliptic equations in 2-dimensions with exponential nonlinearities are constructed. The strategy is to introduce a model…

We consider a conjectured topological inequality for the number of equisingular moduli of a rational surface singularity, and prove it in some natural special cases. When the resolution dual graph is "sufficiently negative" (in a precise…

For a normal F-finite variety $X$ and a boundary divisor $\Delta$ we give a uniform description of an ideal which in characteristic zero yields the multiplier ideal, and in positive characteristic the test ideal of the pair $(X,\Delta)$.…

Near every point of a real-analytic set in $\mathbb R^n$, we make use of Hironaka's resolution of singularity theorem to construct a family of continuous functions in $W^{1, 1}_{loc}$ such that their weak derivatives have (removable)…

Given a collection of $t$ subspaces in an $n$-dimensional $\mathbb{K} $-vector space $W$ we can associate to them $t$ vanishing ideals in the symmetric algebra $\mathcal{S}(W^*) = \mathbb{K}[x_1,x_2,\dots,x_n]$. As a subspace is defined by…

The primary goal of this paper is to provide a general multiplicity estimate. Our main theorem allows to reduce a proof of multiplicity lemma to the study of ideals stable under some appropriate transformation of a polynomial ring. In…

We show the compatibility between the moderate or nearby cycle functor for regular holonomic $\mathcal{D}$-modules, as defined by Beilinson, Kashiwara and Malgrange, and the Hermitian duality functor, as defined by Kashiwara.

Singularities of even smooth functions are studied. A classification of singular points which appear in typical parametric families of even functions with at most five parameters is given. Bifurcations of singular points near a caustic…

Dominant areas of computer science and computation systems are intensively linked to the hypercube-related studies and interpretations. This article presents some transformations and analytics for some example algorithms and Boolean domain…

A symmetric characteristic singular integral equation with two fixed singularities at the endpoints in the class of functions bounded at the ends is analyzed. It reduces to a vector Hilbert problem for a half-disc and then to a vector…

Given a variety $X$ over a perfect field, we study the partition defined on $X$ by the multiplicity (into equimultiple points), and the effect of blowing up at smooth equimultiple centers. Over fields of characteristic zero we prove…

In this paper, a geometric resolution of singularities algorithm is developed. This method is elementary in its statement and proof, using explicit coordinate systems as much as possible. Each coordinate change used in the resolution…

We investigate the problem when the tensor functor by a bimodule yields a singular equivalence. It turns out that this problem is equivalent to the one when the Hom functor given by the same bimodule induces a triangle equivalence between…

We classify entire positive singular solutions to a family of critical sixth order equations in the punctured space with a non-removable singularity at the origin. More precisely, we show that when the origin is a non-removable singularity,…

We establish an algorithm for resolution of singularities of an idealistic filtration in dimension 3 (at the local level) in positive characteristic, incorporating the method recently developed by Benito-Villamayor into our framework.…

This paper is devoted to the analysis of linear second order discrete-time descriptor systems (or singular difference equations (SiDEs) with control). Following the algebraic approach proposed by Kunkel and Mehrmann for pencils of matrix…