Browsing by MSC "32"
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Analytic Varieties with Finite Volume Amoebas are Algebraic
[OWP201133] (Mathematisches Forschungsinstitut Oberwolfach, 2011)In this paper, we study the amoeba volume of a given $k$dimensional generic analytic variety $V$ of the complex algebraic torus $(C^*)^n$. When $n>=2k$, we show that $V$ is algebraic if and only if the volume of its amoeba ... 
Criteria for Algebraicity of Analytic Functions
[OWP201825] (Mathematisches Forschungsinstitut Oberwolfach, 20181112)We consider functions defined on an open subset of a nonsingular, either real or complex, algebraic set. We give criteria for an analytic function to be a Nash (resp. regular, resp. polynomial) function. Our criteria depend ... 
Demailly’s Notion of Algebraic Hyperbolicity: Geometricity, Boundedness, Moduli of Maps
[OWP201820] (Mathematisches Forschungsinstitut Oberwolfach, 20181008)Demailly's conjecture, which is a consequence of the GreenGriffithsLang conjecture on varieties of general type, states that an algebraically hyperbolic complex projective variety is Kobayashi hyperbolic. Our aim is to ... 
Freeness of MultiReflection Arrangements via Primitive Vector Fields
[OWP201710] (Mathematisches Forschungsinstitut Oberwolfach, 20170420)In 2002, Terao showed that every reflection multiarrangement of a real reflection group with constant multiplicity is free by providing a basis of the module of derivations. We first generalize Terao's result to ... 
A Function Algebra Providing New Mergelyan Type Theorems in Several Complex Variables
[OWP201902] (Mathematisches Forschungsinstitut Oberwolfach, 20190211)For compact sets $K\subset \mathbb C^{d}$, we introduce a subalgebra $A_{D}(K)$ of $A(K)$, which allows us to obtain Mergelyan type theorems for products of planar compact sets as well as for graphs of functions. 
Global Variants of Hartogs' Theorem
[OWP201824] (Mathematisches Forschungsinstitut Oberwolfach, 20181106)Hartogs' theorem asserts that a separately holomorphic function, defined on an open subset of $\mathbb{C}^n$, is holomorphic in all the variables. We prove a global variant of this theorem for functions defined on an open ... 
Gradient Canyons, Concentration of Curvature, and Lipschitz Invariants
[OWP201735] (Mathematisches Forschungsinstitut Oberwolfach, 20171213)We find new biLipschitz invariants of holomorphic functions of two variables by using the gradient canyons and by combining analytic and geometric viewpoints on the concentration of curvature. 
Inductive Freeness of Ziegler’s Canonical Multiderivations for Reflection Arrangements
[OWP201714] (Mathematisches Forschungsinstitut Oberwolfach, 20170430)Let $A$ be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction $A''$ of $A$ to any hyperplane endowed with the natural multiplicity is then a free multiarrangement. We initiate a study of the stronger ... 
Milnor fibre homology via deformation
[OWP201522] (Mathematisches Forschungsinstitut Oberwolfach, 2015)In case of onedimensional singular locus, we use deformations in order toget refined information about the Betti numbers of the Milnor fibre. 
A new counting function for the zeros of holomorphic curves
[OWP200925] (Mathematisches Forschungsinstitut Oberwolfach, 20090318)Let $f_1,..., f_p$ be entire functions that do not all vanish at any point, so that $(f_1,..., f_p)$ is a holomorphic curve in $\mathbb{CP}^{p1}$. We introduce a new and more careful notion of counting the order of the ... 
Nonintegrated defect relation for meromorphic maps of complete Kähler manifolds into a projective variety intersecting hypersurfaces
[OWP201019] (Mathematisches Forschungsinstitut Oberwolfach, 2010)In 1985, Fujimoto established a nonintegrated defect relation for meromorphic maps of complete Kähler manifolds into the complex projective space intersecting hyperplanes in general position. In this paper, we generalize ... 
Numerical Invariants and Moduli Spaces for Line Arrangements
[OWP201702] (Mathematisches Forschungsinstitut Oberwolfach, 20170201)Using several numerical invariants, we study a partition of the space of line arrangements in the complex projective plane, given by the intersection lattice types. We offer also a new characterization of the free plane ... 
On the Directionally Newtonnondegenerate Singularities of Complex Hypersurfaces
[OWP200816] (Mathematisches Forschungsinstitut Oberwolfach, 2008)We introduce a minimal generalization of Newtonnondegenerate singularities of hypersurfaces. Roughly speaking, an isolated hypersurface singularity is called directionally Newtonnondegenerate if the local embedded ... 
On the geometry of regular maps from a quasiprojective surface to a curve
[OWP201303] (Mathematisches Forschungsinstitut Oberwolfach, 20130314)We explore consequences of the triviality of the monodromy group, using the condition of purity of the mixed Hodge structure on the cohomology of the surface X. 
On the nonanalyticity locus of an arcanalytic function
[OWP200903] (Mathematisches Forschungsinstitut Oberwolfach, 20090221)A function is called arcanalytic if it is real analytic on each real analytic arc. In real analytic geometry there are many examples of arcanalytic functions that are not real analytic. Arc analytic functions appear ... 
On the δ=const Collisions of Singularities of Complex Plane Curves
[OWP200815] (Mathematisches Forschungsinstitut Oberwolfach, 2008)We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equinormalizable or ... 
Rational Approximation on Products of Planar Domains
[OWP201605] (Mathematisches Forschungsinstitut Oberwolfach, 20160617)We consider $A(\Omega)$, the Banach space of functions $f$ from $ \overline{\Omega}=\prod_{i \in I} \overline{U_i}$ to $\mathbb{C}$ that are continuous with respect to the product topology and separately holomorphic, where ... 
Real Analyticity is Concentrated in Dimension 2
[OWP201823] (Mathematisches Forschungsinstitut Oberwolfach, 20181105)We prove that a realvalued function on a real analytic manifold is analytic whenever all its restrictions to $2$dimensional analytic submanifolds are analytic functions. We also obtain analogous results in the framework ... 
Second Main Theorems and Unicity of Meromorphic Mappings with Moving Hypersurfaces
[OWP201138] (Mathematisches Forschungsinstitut Oberwolfach, 2011)In this article, we establish some new second main theorems for meromorphic mappings of $\mathbf{C}^m$ into $\mathbf{P}^n(\mathbf{C})$ and moving hypersurfaces with truncated counting functions. As an application, we prove ... 
Spherical ArcLength as a Global Conformal Parameter for Analytic Curves in the Riemann Sphere
[OWP201621] (Mathematisches Forschungsinstitut Oberwolfach, 20161111)We prove that for every analytic curve in the complex plane $\mathbb{C}$, Euclidean and spherical arclengths are global conformal parameters. We also prove that for any analytic curve in the hyperbolic plane, hyperbolic ...