Related papers: Partial local resolution by characteristic zero me…
The scaled boundary finite element method is known for its capability in reproducing highly-detailed solution fields. This, however, is only attainable in those cases where analytical solutions exist. Many others invoke the use of numerical…
We consider the semilinear wave equation with power nonlinearity in one space dimension. We consider an arbitrary blow-up solution $u(x,t)$, the graph $x\mapsto T(x)$ of its blow-up points and ${\cal S}\subset {\mathbb R}$ the set of all…
The seminal concept of characteristic polygon of an embedded algebroid surface, first developed by Hironaka, seems well suited for combinatorially (perhaps even effectively) tracking of a resolution process. However, the way this object…
The object of the present is a proof of the existence of functorial resolution of tame quotient singularities for quasi-projective varieties over algebraically closed fields.
We are concerned with the qualitative analysis of positive singular solutions with blow-up boundary for a class of logistic-type equations with slow diffusion and variable potential. We establish the exact blow-up rate of solutions near the…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
In this paper, we investigate the asymptotic behaviors of solutions to the singular Yamabe problem with negative constant scalar curvature near singular boundaries and derive optimal estimates, where the background metrics are not assumed…
We introduce conditions on cones of normal toric varieties under which the polyhedron defining the normalized Nash blowup does not depend on the characteristic of the base field. As a consequence, we deduce several results on the resolution…
We prove sharp blow up rates of solutions of higher order conformally invariant equations in a bounded domain with an isolated singularity, and show the asymptotic radial symmetry of the solutions near the singularity. This is an extension…
Let $M$ be a complex- or real-analytic manifold, $\theta$ be a singular distribution and $\mathcal{I}$ a coherent ideal sheaf defined on $M$. We prove the existence of a local resolution of singularities of $\mathcal{I}$ that preserves the…
We extend the classical formula of Porteous for blowing-up Chern classes to the case of blow-ups of possibly singular varieties along regularly embedded centers. The proof of this generalization is perhaps conceptually simpler than the…
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…
In this paper, we consider positively graded isolated non F-rational singularities (R,m) with d=dim R over the field K of positive characteristic. We give a representation of lower local cohomologies H^i_m(R) (i<d) in terms of tight closure…
In this paper, we study the properties of averaged fundamental solutions of a special type for Laplace operators in the Euclidean space of an arbitrary dimension. We consider a class of kernels suitable for probabilistic averaging, and…
The problem of resolution of singularities in positive characteristic can be reformulated as follows: Fix a hypersurface $X$, embedded in a smooth scheme, with points of multiplicity at most $n$. Let an $n$-sequence of transformations of…
We initiate the study of the resolution of singularities properties of Nash blowups over fields of prime characteristic. We prove that the iteration of normalized Nash blowups desingularizes normal toric surfaces. We also introduce a prime…
The subject is partial desingularization preserving the normal crossings singularities of an algebraic or analytic variety X (over the complex field or over an uncountable algebraically closed field of characteristic zero, in the algebraic…
In this survey paper we give an overview on some aspects of singularities of algebraic varieties over an algebraically closed field of arbitrary characteristic. We review in particular results on equisingularity of plane curve…
In certain extensions of General Relativity, wormholes generated by spherically symmetric electric fields can resolve black hole singularities without necessarily removing curvature divergences. This is shown by studying geodesic…
This paper is devoted to give all the technical constructions and definitions that will lead to the construction of an algorithm of resolution of singularities for binomial ideals. We construct a resolution function that will provide a…