Related papers: Logarithmic resolution via multi-weighted blow-ups
We address the question of normal-crossings-preserving resolution of singularities (NC-preserving resolution), and compare the cases of characteristic 0 and characteristic 2. In characteristic 0, it is shown by Belotto da Silva and…
In this paper we apply Shokurov's inductive method to study terminal and canonical singularities. As an easy consequence of the Minimal Model Program we show that for any three-dimensional log terminal singularity there exists some special,…
We provide an efficient method of blowing up to compute leading order contributions of the recently introduced stringy canonical forms. The method is related to the well-known Hironaka's polyhedra game, and the given algorithm is also…
The logarithmic Hilbert scheme of a logarithmic curve parametrizes subschemes on the expanded degenerations of the curve that are transverse to the boundary. We prove that the logarithmic Hilbert scheme of points on a smooth pointed curve…
Raynaud and Gruson developed the theory of blowing-up an algebraic variety $X$ along a coherent sheaf $M$ in the sense that there exists a blow-up $X'$ of $X$ such that the "strict transform" of $M$ is flat over $X'$ and the blow-up…
An algorithm for resolution of singularities in characteristic zero is described. It is expressed in terms of multi-ideals, that essentially are defined as a finite sequence of pairs, each one consiting of a sheaf of ideals and a positive…
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…
We establish existence of functorial orbifold reductions of singularities for Poisson subvarieties in smooth Poisson threefolds. Namely, we show that with enough weighted blowups, one can reduce the singularities of such Poisson…
We present a hypersurface singularity in positive characteristic which is defined by a purely inseparable power series, and a sequence of point blowups so that, after applying the blowups to the singularity, the same type of singularity…
In this paper we simplify and otherwise improve the local resolution of singularities algorithm of [G1]-[G3], providing a local resolution of singularities method that works for functions with convergent power series over an arbitrary local…
In this paper we give a necessary combinatorial condition for a negative--definite plumbing tree to be suitable for rational blow--down, or to be the graph of a complex surface singularity which admits a rational homology disk smoothing.…
We establish the optimal regularity for solutions to the multiple membranes problem, and perform a blow-up analysis at points on the free boundary with the highest multiplicity. This leads to a complete classification of blow-up profiles in…
We consider singular solutions of the biharmonic NLS. In the L^2-critical case, the blowup rate is bounded by a quartic-root power law, the solution approaches a self-similar profile, and a finite amount of L^2-norm, which is no less than…
We give a simplified algorithm of the functorial weak factorization of birational morphisms of nonsingular varieties over a field of characteristic zero into a composite of blow-ups and blow-downs with smooth centers.
In their work on a sharp compactness theorem for the Yamabe problem, Khuri, Marques and Schoen apply a refined blow-up analysis (what we call `second order blow-up argument' in this article) to obtain highly accurate approximate solutions…
In this paper, we attempt to resolve the singularities of the zero variety of a $C^{\infty}$ function of two variables as much as possible by using ordinary blowings up. As a result, we formulate an algorithm to locally express the zero…
These lecture notes provide a unified overview of most known canonical desingularization methods in characteristic zero. It starts with discussing the classical method, and then proceeds with the recently discovered ones: logarithmic…
In this note we try to understand the blow-up of solutions to Nakao's problem by using nonlinear ordinary differential inequalities.
Real blow-up, including inhomogeneous versions, of boundary faces of a manifold (with corners) is an important tool for resolving singularities, degeneracies and competing notions of homogeneity. These constructions are shown to be…
We study the possible regularization of collision solutions for one centre problems with a weak singularity. In the case of logarithmic singularities, we consider the method of regularization via smoothing of the potential. With this…