On fundamental groups of algebraic varieties and value distribution theory

Katsutoshi Yamanoi

Displaying similar documents to “On fundamental groups of algebraic varieties and value distribution theory”

On the Briançon-Skoda theorem on a singular variety

Mats Andersson, Håkan Samuelsson, Jacob Sznajdman (2010)

Annales de l’institut Fourier

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Let $Z$ be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform Briançon-Skoda theorem for the local ring $𝒪_{Z}$ ; a result which was previously proved by Huneke by algebraic methods. For ideals with few generators we also get much sharper results.

Deformation of holomorphic maps onto Fano manifolds of second and fourth Betti numbers 1

Jun-Muk Hwang (2007)

Annales de l’institut Fourier

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Let $X$ be a Fano manifold with $b_{2} = 1$ different from the projective space such that any two surfaces in $X$ have proportional fundamental classes in $H_{4} (X, C)$ . Let $f : Y \to X$ be a surjective holomorphic map from a projective variety $Y$ . We show that all deformations of $f$ with $Y$ and $X$ fixed, come from automorphisms of $X$ . The proof is obtained by studying the geometry of the integral varieties of the multi-valued foliation defined by the variety of minimal rational tangents of $X$ .

Uniqueness in Rough Almost Complex Structures, and Differential Inequalities

Jean-Pierre Rosay (2010)

Annales de l’institut Fourier

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The study of $J$ -holomorphic maps leads to the consideration of the inequations $| \frac{\partial u}{\partial \bar{z}} | \leq C | u |$ , and $| \frac{\partial u}{\partial \bar{z}} | \leq ϵ | \frac{\partial u}{\partial z} |$ . The first inequation is fairly easy to use. The second one, that is relevant to the case of rough structures, is more delicate. The case of $u$ vector valued is strikingly different from the scalar valued case. Unique continuation and isolated zeroes are the main topics under study. One of the results is that, in almost complex structures of Hölder class $\frac{1}{2}$ , any $J$ -holomorphic curve that is constant on...

On Bochner-Martinelli residue currents and their annihilator ideals

Mattias Jonsson, Elizabeth Wulcan (2009)

Annales de l’institut Fourier

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We study the residue current $R^{f}$ of Bochner-Martinelli type associated with a tuple $f = (f_{1}, \dots, f_{m})$ of holomorphic germs at $0 \in C^{n}$ , whose common zero set equals the origin. Our main results are a geometric description of $R^{f}$ in terms of the Rees valuations associated with the ideal $(f)$ generated by $f$ and a characterization of when the annihilator ideal of $R^{f}$ equals $(f)$ .

Extension of holomorphic maps between real hypersurfaces of different dimension

Rasul Shafikov, Kausha Verma (2007)

Annales de l’institut Fourier

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In this paper we extend the results on analytic continuation of germs of holomorphic mappings from a real analytic hypersurface to a real algebraic hypersurface to the case when the target hypersurface is of higher dimension than the source. More precisely, we prove the following: Let $M$ be a connected smooth real analytic minimal hypersurface in $C^{n}$ , $M^{'}$ be a compact strictly pseudoconvex real algebraic hypersurface in $C^{N}$ , $1 < n \leq N$ . Suppose that $f$ is a germ of a holomorphic map at a point $p$ in $M$ ...