Related papers: Notes on Nash modification

Real blow-ups and more refined "zooms" play a key role in the analysis of singularities of complex-analytic differential modules. They do not change the underlying topology, but the uniform structure. This suggests to revisit the cohomology…

There are several ways to generalize characteristic classes for singular algebraic varieties. The simplest ones to describe are Chern-Mather classes obtained by Nash blow up. They serve as an ingredient to construct…

Let X be a singular real rational surface obtained from a smooth real rational surface by performing weighted blow-ups. Denote by Aut(X) the group of algebraic automorphisms of X into itself. Let n be a natural integer and let…

Polymorphism, the phenomenon that a species can exist in many discrete forms, is common in nature, such as hair colors in an animal species, flower colors in a tree species, and blood types in humans, etc. In materials science, it refers to…

In this paper we investigate realization theory of a class of non-linear systems, called Nash systems. Nash systems are non-linear systems whose vector fields and readout maps are analytic semi-algebraic functions. In this paper we will…

We introduce in a reduced complex space, a "new coherent sub-sheaf" of the sheaf $\omega\_{X}^{\bullet}$ which has the "universal pull-back property" for any holomorphic map, and which is in general bigger than the usual sheaf of…

Resolution of singularities of varieties over fields of characteristic zero can be proved by using the multiplicity as main invariant. The proof of this result leads to new questions in positive characteristic. We discuss here results which…

It has been recently shown that the iteration of Nash modification on not necessarily normal toric varieties corresponds to a purely combinatorial algorithm on the generators of the semigroup associated to the toric variety. We will show…

Suppose that $\Phi:X\to Y$ is a morphism from a 3 fold to a surface (over an algebraically closed field of characteristic zero). We prove that there exist sequences of blowups of nonsingular subvarieties $X_1\to X$ and $Y_1\to Y$ such that…

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 classify the pairs $(X,\pi)$, where $\pi\colon X\to S$ is a $\mathbb{P}^1$-bundle over a non-rational geometrically ruled surface $S$ and $\mathrm{Aut}^\circ(X)$ is relatively maximal, i.e., maximal with respect to the inclusion in the…

Let G be an algebraic group and let X be a generically free G-variety. We show that X can be transformed, by a sequence of blowups with smooth G-equivariant centers, into a G-variety X' with the following property: the stabilizer of every…

In this paper we investigate the relation betwen the Nash modification and the Bi-Lipschtiz equivalent germs in the cases of two germs and for a family of hypersurfaces with isolated singularities.

Let $\pi :X\rightarrow \mathbb{P}^3$ be a finite composition of blowups along smooth centers. We show that for "almost all" of such $X$, if $f\in Aut(X)$ then its first and second dynamical degrees are the same. We also construct many…

We prove a monomialization theorem for mappings in general classes of infinitely differentiable functions that are called quasianalytic. Examples include Denjoy-Carleman classes, the class of $\cC^\infty$ functions definable in a…

Let $k$ be a field, $X$ a connected scheme proper over $k$, $D\subsetneq X$ an ample effective connected divisor, $x\in D(k)$. For Tannakian categories $\mathcal{C}_X$ and $\mathcal{C}_D$ whose objects consist of vector bundles on $X$ and…

Let $\Sym^m X$ denote the $m$-th symmetric power of a smooth projective curve $X$. Let $\wt{\Sym^m X}$ be the blow up of $\Sym^m X$ along some non-singular subvariety. In this note we are going to discuss when the pushforward homomorphism…

Let $p$ be a prime integer and $F$ a field of characteristic 0. Let $X$ be the {\em norm variety} of a symbol in the Galois cohomology group $H^{n+1}(F,\mu_p^{\otimes n})$ (for some $n\geq1$), constructed in the proof of the Bloch-Kato…

Let $(X,O)$ be a germ of a normal surface singularity, $\pi : \tilde X\longrightarrow X$ be the minimal resolution of singularities and let $A=(a_{i,j})$ be the $n\times n$ symmetrical intersection matrix of the exceptional set of $\tilde…

This paper obtains criteria for a Fano variety X with normal crossing singularities defined over an algebraically closed field of characteristic zero, to be smoothable. The difference with the original version is that the theory of…