Related papers: B\"ottcher coordinates
A class of C*-algebras is described for which the homomorphism from $C_0(0,1]$ to the algebra may be classified by means of the Cuntz semigroup functor. Examples are given of algebras--simple and non-simple--for which this classification…
Systems of germs of sets in infinite-dimensional spaces are introduced and studied. Such a system corresponds to a local zero-set of an ideal of the ring of analytic functions of infinite number of variables. Conversely, this system of…
The singularity space consists of all germs $(X,x)$, with $X$ a Noetherian scheme and $x$ a point, where we identify two such germs if they become the same after an analytic extension of scalars. This is a Polish space for the metric given…
In this paper we introduce new classes of gluing of complex analytic spaces germs, called weakly large, large and strongly large. We give a description of their Poincar\'e series and, as applications, we give numerical criteria to determine…
This note provides some technical support to the proof of a result of W. Winter which shows that two unital separable simple amenable ${\cal Z}$-absorbing C*-algebras with locally finite decomposition property satisfying the UCT whose…
We introduce a new point of view towards Glaeser's theorem on composite $C^\infty$ functions [Ann. of Math. 1963], with respect to which we can formulate a ``$C^k$ composite function property" that is satisfied by all semiproper real…
We prove an analog of the flower theorem for non-degenerate reduced tangent to the identity germs that fix the coordinate hyperspaces in any dimension.
The paper deals with Henselian valued field with analytic structure. Actually, we are focused on separated analytic structures, but the results remain valid for strictly convergent analytic ones as well. A classical example of the latter is…
Let (X,0) be a germ of complex analytic normal variety, non-singular outside 0. An essential divisor over (X,0) is a divisorial valuation of the field of meromorphic functions on (X,0), whose center on any resolution of the germ is an…
We propose, within the context of the dynamics of a holomorphic germ in CI^N, a definition of 'attracting basin' of a fixed point. We prove that the inverse germ of an endomorphism of CI^N with a repulsive fixed point in 0, satisfying a…
In this paper we introduce and study the ''convergent'' algebra (containing ''a'' and ''b'' and acting on holomorphic germs in ''a'') which naturally acts on the ''generalized Brieskorn modules'' associated to the Gauss-Manin connections of…
Let $\Gamma $ be a $C^\infty $ curve in $\Bbb{C}$ containing 0; it becomes $\Gamma_\theta $ after rotation by angle $\theta $ about 0. Suppose a $C^\infty $ function $f$ can be extended holomorphically to a neighborhood of each element of…
We establish some algebraic properties of the group $\mathrm{Diff}(\mathbb{C}^n,0)$ of germs of analytic diffeomorphisms of $\mathbb{C}^n$, and its formal completion $\widehat{\mathrm{Diff}}(\mathbb{C}^n,0)$. For instance we describe the…
The B\^{o}cher-Grace Theorem can be stated as follows: Let $p$ be a third degree complex polynomial. Then there is a unique inscribed ellipse interpolating the midpoints of the triangle formed from the roots of $p$, and the foci of the…
In this article we prove that every germ of analytic meromorphic function at $(\mathbb{C}^{2},0)$ is equivalent, under the right composition by a germ of biholomorphism, to a germ of algebraic meromorphic function. An analogous result is…
In this paper we introduce an exponential map of the algebra of germs of vector fields into the group of germs of diffeomorphisms at zero. It is shown that this mapping is not a bijection. A brief review of the key results of the analytic…
To an arbitrary directed graph we associate a row-finite directed graph whose C*-algebra contains the C*-algebra of the original graph as a full corner. This allows us to generalize results for C*-algebras of row-finite graphs to…
We classify generic unfoldings of germs of antiholomorphic diffeomorphisms with a parabolic point of codimension~$k$ (i.e.~a fixed point of multiplicity $k+1$) under conjugacy. Such generic unfoldings depend real analytically on $k$ real…
We give the definition of the Thom condition and we show that given any germ of complex analytic function $f:(X,x)\to(\mathbb{C},0)$ on a complex analytic space $X$, there exists a geometric local monodromy without fixed points, provided…
To a given analytic function germ $f:(\mathbb{R}^d,0) \to (\mathbb{R},0)$, we associate zeta functions $Z_{f,+}$, $Z_{f,-} \in \mathbb{Z} [[T]]$, defined analogously to the motivic zeta functions of Denef and Loeser. We show that our zeta…