Related papers: Algorithmic resolution via weighted blowings up

In 2019, Abramovich--Temkin--Wlodarczyk and McQuillan used weighted blow-ups to obtain very fast and functorial algorithms for resolution of singularities in characteristic zero. Recently, Abramovich--Quek--Schober simplified the…

We provide a procedure for resolving, in characteristic 0, singularities of a variety $X$ embedded in a smooth variety $Y$ by repeatedly blowing up the worst singularities, in the sense of stack-theoretic weighted blowings up. No history,…

In characteristic zero, we construct logarithmic resolution of singularities, with simple normal crossings exceptional divisor, using weighted blow-ups.

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 show that stack-theoretic resolution of singularities preserving normal crossings (partial desingularization) by weighted blowings-up, can be obtained in a simple direct way from a splitting theorem of the first and third authors, using…

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…

Let $X$ be a fs logarithmic scheme that is generically logarithmically smooth, and that admits a strict closed embedding into a logarithmically smooth scheme $Y$ over a field $\kk$ of characteristic zero. We construct a simple and fast…

We discuss to what extent the local techniques of resolution of singularities over fields of characteristic zero can be applied to improve singularities in general. For certain interesting classes of singularities, this leads to an embedded…

This article is an exposition of an elementary constructive proof of canonical resolution of singularities in characteristic zero, presented in detail in Invent. Math. 128 (1997), 207-302. We define a new local invariant and get an…

Stack-theoretic blow-ups have proven to be efficient in resolving singularities over fields of characteristic zero. In this article, we move forward towards positive characteristic where new challenges arise. In particular, the dimension of…

Geometric treatments of blow-up solutions for autonomous ordinary differential equations and their blow-up rates are concerned. Our approach focuses on the type of invariant sets at infinity via compactifications of phase spaces, and…

We prove the existence of resolution of singularities for arbitrary (not necessarily reduced or irreducible) excellent two-dimensional schemes, via permissible blow-ups. The resolution is canonical, and functorial with respect to…

I begin by explaining to non-specialists why resolution of singularities in characteristic 0 works. Then I go into some ideas telling how it actually works. I finish with a brief discussion of related results on foliations. I report on work…

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.…

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…

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…

This paper formulates an elementary algorithm for resolution of singularities in a neighborhood of a singular point over a field of characteristic zero. The algorithm is composed of finite sequences of Newton polyhedra and monomial…

We formulate a resolution of singularities algorithm for analyzing the zero sets of real-analytic functions in dimensions $\geq 3$. Rather than using the celebrated result of Hironaka, the algorithm is modeled on a more explicit and…

Given a singular hypersurface in a regular 2-dimensional scheme essentially of finite type over a field, we construct an embedded resolution of singularities by weighted blow-ups. This differs from our earlier work which required…

Categorical resolution of singularities has been constructed in arXiv:1212.6170. It proceeds by alternating two steps of seemingly different nature. We show how to use the formalism of filtered derived categories to combine the two steps…