Related papers: Algorithmic equiresolution of deformations of embe…
This paper studies the concept of algorithmic equiresolution of a family of embedded varieties or ideals, which means a simultaneous resolution of such a family compatible with a given (suitable) algorithm of resolution in characteristic…
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…
Given an algorithm of resolution of singularities satisfying certain conditions (``good algorithms''), natural notions of simultaneous algorithmic resolution, or equiresolution, for families of embedded schemes (parametrized by a reduced…
We give a combinatorial algorithm for equivariant embedded resolution of singularities of a toric variety defined over a perfect field. The algorithm is realized by a finite succession of blowings-up with smooth invariant centres that…
We introduce the notion of a simultaneous categorical resolution of singularities, a categorical version of simultaneous resolutions of rational double points of surface degenerations. Furthermore, we suggest a construction of simultaneous…
We show that the derived category of any singularity over a field of characteristic 0 can be embedded fully and faithfully into a smooth triangulated category which has a semiorthogonal decomposition with components equivalent to derived…
We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.
We build two embedded resolution procedures of a quasi-ordinary singularity of complex analytic hypersurface, by using toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection of the…
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…
A key example in Borger's theory of $\Lambda$-structure is toric $\Lambda$-structure. We prove a resolution of singularities result for embedded toric $\Lambda$-schemes by applying an algorithm of Bierstone and Milman for toric varieties…
We show that for two afii varieties over an arbitrary field of characteristic zero, there is no general form of an algorithm for checking the presence of an embedding of one algebraic variety in another. Moreover, we establish this for…
We compare some algebras appeared in the recent attempts to prove resolution of singularities in positive characteristic. We also construct an algebra which encodes the same information and it is equivalent, up to integral closure, to the…
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…
We discuss recent developments in the study of semiorthogonal decompositions of algebraic varieties with an emphasis on their behaviour in families. First, we overview new results concerning homological projective duality. Then we introduce…
We discuss Hironaka's theorem on resolution of singularities in charactetistic 0 as well as more recent progress, both on simplifying and improving Hironaka's method of proof and on new results and directions on families of varieties,…
We unify problems about the equivariant geometry of symmetric quiver representation varieties, in the finite type setting, with the corresponding problems for symmetric varieties $GL(n)/K$ where $K$ is an orthogonal or symplectic group. In…
We give a new proof of the simultaneous embedded local uniformization Theorem in zero characteristic for essentially of finite type rings and for quasi excellent rings. The results are a consequence of the simultaneaous monomialization…
A new proof of equivariant resolution of singularities under a finite group action in characteristic 0 is provided. We assume we know how to resolve singularities without group action. We first prove equivariant resolution of toroidal…
In this paper we construct a combinatorial algorithm of resolution of singularities for binomial ideals, over a field of arbitrary characteristic. This algorithm is applied to any binomial ideal. This means ideals generated by binomial…
The purpose, mainly expository and speculative, of this paper---an outgrowth of a survey lecture at the September 1997 Obergurgl working week---is to indicate some (not all) of the efforts that have been made to interpret equisingularity,…