相关论文: Formal Desingularization of Surfaces - The Jung Me…
In a previous article, the authors developed two conversion methods to improve the $\Sigma$-method for structural analysis (SA) of differential-algebraic equations (DAEs). These methods reformulate a DAE on which the $\Sigma$-method fails…
Renormalization is a well-known technique to get rid of ultraviolet (UV) singularities. When relying on Dimensional Regularization (DREG), these become manifest as $\epsilon$-poles, allowing to define counter-terms with useful recursive…
This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construc-tion uses a single linear differential form defined from the…
We review and compare different computational variational methods applied to a system of fourth order equations that arises as a model of cylinder buckling. We describe both the discretization and implementation, in particular how to deal…
We address the following question of partial desingularization preserving normal crossings. Given an algebraic (or analytic) variety X in characteristic zero, can we find a finite sequence of blowings-up preserving the normal-crossings…
A graph profile records all possible densities of a fixed finite set of graphs. Profiles can be extremely complicated; for instance the full profile of any triple of connected graphs is not known, and little is known about hypergraph…
We extend to pairs classical results of R. Elkik on lifting of homomorphisms and algebraization. In particular, we establish algebraization of an affine rig-smooth formal variety with a rig-smooth closed subvariety. This solves…
Umbral theory, formulated in its modern version by S. Roman and G.~C. Rota, has been reconsidered in more recent times by G. Dattoli and collaborators with the aim of devising a working computational tool in the framework of special…
Dlab--Ringel's standardization method gives a realization of a standardly stratified algebra. In this paper, we construct mixed stratified algebras, which are a generalization of standardly stratified algebras, following Dlab--Ringel's…
In this paper, local monomialization theorems are proven for analytic morphisms of complex and real analytic spaces. This gives the generalization of the local monomialization theorem for morphisms of algebraic varieties over a field of…
Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the…
This is a second part of alg-geom/9611015. We construct a natural hyperkaehler desingularization for all singular hyperkaehler varieties. The desingularization theorem was proven in alg-geom/9611015 under additional assumption of local…
This paper is divided into two parts. The first is a review, through categorical lenses, of the classical theory of regular-singular differential systems over $C((x))$ and $\mathbb P^1_C\smallsetminus\{0,\infty\}$, where $C$ is…
Inspired by a construction by Arnaud Beauville of a surface of general type with $K^2 = 8, p_g =0$, the second author defined the Beauville surfaces as the surfaces which are rigid, i.e., they have no nontrivial deformation, and admit un…
An algorithmic proof of the General Neron Desingularization theorem is given for $2$-dimensional local rings and morphisms with small singular locus.
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…
The main goal of this paper is to introduce a framework for infinitesimal deformation problems, using new methods coming from operadic calculus. We construct an adjunction between infinitesimal deformation problems over some type of…
In this article, we discuss formal invariants of singularly-perturbed linear differential systems in neighborhood of turning points and give algorithms which allow their computation. The algorithms proposed are implemented in the computer…
We present a generalized reduction procedure which encompasses the one based on the momentum map and the projection method. By using the duality between manifolds and ring of functions defined on them, we have cast our procedure in an…
We discuss a special class of solutions to the minimal surface system. These are vector-valued functions that "decrease area" and are natural generalization of scalar functions. After defining area-decreasing maps, we show several classical…