相关论文: Flag higher Nash blowups

We prove that intersection multiplicity of two plane curves defined by Fulton's axioms is equivalent to the multiplicity computed using blowup. The algorithm based on the latter is presented and its complexity is estimated. We compute for…

In this paper, we investigate the possibility of constructing isomonodromic deformations of logarithmic connections on curves by using ramified covers. We give new examples and prove a classification result.

This paper deals with the Nash problem, which claims that there are as many families of arcs on a singular germ of surface $U$ as there are essential components of the exceptional divisor in the desingularisation of this singularity. Let…

The present paper concerns with the existence of blow-up solution for a class of elliptic system with convection term. Here, we prove a result involving sub and supersolution for a class of elliptic system whose nonlinearity can depend of…

In a series of papers the authors introduced the so-called blown-up intersection cochains. These cochains are suitable to study products and cohomology operations of intersection cohomology of stratified spaces. The aim of this paper is to…

Surface nanobubbles are nanoscopic spherical-cap shaped gaseous domains on immersed substrates which are stable, even for days. After the stability of a {\it single} surface nanobubble has been theoretically explained, i.e. contact line…

The h-cobordism theorem is a noted theorem in differential and PL topology. A generalization of the h-cobordism theorem for possibly non simply connected manifolds is the so called s-cobordism theorem. In this paper, we prove semialgebraic…

We study twisted cohomologies with paracompactifying families of supports. The Kunneth theorems, Leray-Hirsch theorems and self-intersection formulae are established. Based on these results, we eventually give explicit expressions of…

We first introduce and study the notion of multi-weighted blow-ups, which is later used to systematically construct an explicit yet efficient algorithm for functorial logarithmic resolution in characteristic zero, in the sense of Hironaka.…

We factorize three-dimensional terminal flops into a composition of divisorial contractions to points and blowing-up smooth curves.

We give blow-up analysis for the solutions of an elliptic equation under some conditions. Also, we derive a compactness result for this equation.

In this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed…

This note will become part of a new paper with more authors.

This work proposes a novel set of techniques for approximating a Nash equilibrium in a finite, normal-form game. It achieves this by constructing a new reformulation as solving a parameterized system of multivariate polynomials with tunable…

An algorithmic proof of the General N\'eron Desingularization theorem and its uniform version is given for morphisms with big smooth locus. This generalizes the results for the one-dimensional case.

This paper is devoted to study multiplicity and regularity as well as to present some classifications of complex analytic sets. We present an equivalence for complex analytical sets, namely blow-spherical equivalence and we receive several…

Let $F$ be a one-dimensional holomorphic foliation on $\mathbb{P}^n$ such that $W\subset Sing(F)$, where $W$ is a smooth complete intersection variety. We determine and compute the variation of the Milnor number $ \mu(F, W)$ under blowups,…

The focusing cubic NLS is a canonical model for the propagation of laser beams. In dimensions 2 and 3, it is known that a large class of initial data leads to finite time blow-up. Now, physical experiments suggest that this blow-up does not…

In terms of the gauged nonlinear $\sigma$-models, we describe some results and implications of solving the following problem: Given a smooth symplectic manifold as target space with a quasi-free Hamiltonian group action, perform the…

Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.