Related papers: Functorial embedded resolution via weighted blowin…

The paper is concerned with the three-dimensional electromagnetic scattering from a large open rectangular cavity that is embedded in a perfectly electrically conducting infinite ground plane. By introducing a transparent boundary…

We construct a series of blowups $(\widetilde M_i,\pi_i)_{i\in \mathbb N_0}$ of a singular foliation by applying to the universal Lie $\infty$-algebroid of a singular foliation the so-called Nash modification. For $i=0$, we recover a blowup…

Any Lie algebroid $A$ admits a Nash-type blow-up $\mathrm{Nash}(A)$ that sits in a nice short exact sequence of Lie algebroids $0\rightarrow K\rightarrow \mathrm{Nash}(A)\rightarrow \mathcal{D}\rightarrow 0$ with $K$ a Lie algebra bundle…

The objective of this paper is to discuss invariants of singularities of algebraic schemes over fields of positive characteristic, and to show how they yield the simplification of singularities. We focus here on invariants which arise in an…

We provide explicit criteria for blow-up solutions of autonomous ordinary differential equations. Ideas are based on the quasi-homogeneous desingularization (blowing-up) of singularities and compactifications of phase spaces, which suitably…

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…

We prove existence for many examples of shrinkers by producing compact, smoothly embedded surfaces that, under mean curvature flow, develop singularities at which the shrinkers occur as blowups.

Using Frobenius morphisms of noncommutative blowups, we prove that every normal toric singularity has a standard noncommutative resolution.

We consider in this paper a large class of perturbed semilinear wave equations with critical (in the conformal transform sense) power nonlinearity. We will show that the blow-up rate of any singular solution is given by the solution of the…

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…

Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This work attempts to provide an affirmative answer to…

In this survey we report on some recent results related to various singular phenomena arising in the study of some classes of nonlinear elliptic equations. We establish qualitative results on the existence, nonexistence or the uniqueness of…

For a weighted quasihomogeneous two dimensional hypersurface singularity, we define a smoothing with unipotent monodromy and an isolated graded normal singularity. We study the natural weighted blow up of both the smoothing and the surface.…

We establish the first complete classification of finite-time blow-up scenarios for strong solutions to the three-dimensional incompressible Euler equations with surface tension in a bounded domain possessing a closed, moving free boundary.…

We consider the semilinear wave equation with power nonlinearity in one space dimension. We first show the existence of a blow-up solution with a characteristic point. Then, we consider an arbitrary blow-up solution $u(x,t)$, the graph…

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 construct a functor from the category of manifolds with generalized corners to the category of complexes of toric monoids, and for every `refinement' of the complex associated to a manifold, we show there is a unique `blow-up', i.e., a…

We study development of singularities for the spherically symmetric Yang-Mills equations in $d+1$ dimensional Minkowski spacetime for $d=4$ (the critical dimension) and $d=5$ (the lowest supercritical dimension). Using combined numerical…

We show how blowing up varieties in base loci of linear systems gives a procedure for creating new homological projective duals from old. Starting with a HP dual pair $X,Y$ and smooth orthogonal linear sections $X_L,Y_L$, we prove that the…

In the category of log schemes, it is unclear how to define the blow-ups for non-strict closed immersions. In this article, we introduce the notion of divided log spaces. We obtain the category of divided log spaces by locally inverting log…