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Displaying 61 – 80 of 88

On the Łojasiewicz exponent of the gradient of a holomorphic function

Andrzej Lenarcik (1998)

Banach Center Publications

The Łojasiewicz exponent of the gradient of a convergent power series h(X,Y) with complex coefficients is the greatest lower bound of the set of λ > 0 such that the inequality ${| g r a d h (x, y) | \geq c | (x, y) |}^{λ}$ holds near $0 \in C^{2}$ for a certain c > 0. In the paper, we give an estimate of the Łojasiewicz exponent of grad h using information from the Newton diagram of h. We obtain the exact value of the exponent for non-degenerate series.

On the Milnor fibrations of weighted homogeneous polynomials

Alexandru Dimca (1990)

Compositio Mathematica

On the Mixed Hodge Structure on the Cohomology of the Milnor Fibre.

J. Scherk, J.H.M. Steenbrink (1985)

Mathematische Annalen

On the moderate growth of generalized Dirichlet series for hypoelliptic polynomials

Ben Lichtin (1991)

Compositio Mathematica

On the monodromy at infinity of a polynomial map

R. García López, A. Némethi (1996)

Compositio Mathematica

On the monodromy of curve singularities.

J.H.M. Steenbrink, A. Némethi (1996)

Mathematische Zeitschrift

On the Monodromy Theorem for Isolated Hypersurface Singularities.

John Scherk (1980)

Inventiones mathematicae

On the motivic measure on the space of functions.

Eugeny Gorsky (2007)

Revista Matemática Complutense

On the multiplicity of a quasi-homogeneous isolated singularity.

Sȩkalsi, Maciej (2008)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

On the Ozsváth-Szabó invariant of negative definite plumbed 3-manifolds.

Némethi, András (2005)

Geometry & Topology

On the real secondary classes of transversely holomorphic foliations

Taro Asuke (2000)

Annales de l'institut Fourier

In this paper we study the real secondary classes of transversely holomorphic foliations. We define a homomorphism from the space $H^{*} ({WO}_{2 q})$ of the real secondary classes to the space $H^{*} ({WU}_{q})$ of the complex secondary classes that corresponds to forgetting the transverse holomorphic structure. By using this homomorphism we show, for example, the decomposition of the Godbillon-Vey class into the imaginary part of the Bott class and the first Chern class of the complex normal bundle of the foliation. We show also...

On the string-theoretic Euler numbers of 3-dimensional $A$ - $D$ - $E$ singularities.

Dais, Dimitrios I., Roczen, Marko (2001)

Advances in Geometry

On the structure of Brieskorn lattice

Morihiko Saito (1989)

Annales de l'institut Fourier

We study the structure of the filtered Gauss-Manin system associated to a holomorphic function with an isolated singularity, and get a basis of the Brieskorn lattice $Ω_{X, 0}^{n + 1} / d f \land d Ω_{X, 0}^{n + 1}$ over $ℂ {{\partial_{t}^{- 1}}}$ such that the action of $t$ is expressed by $t v = A_{0} + A_{1} \partial_{t}^{- 1} v$ for two matrices $A_{0}, A_{1}$ with $A_{1}$ semi-simple, where $v =^{t} (v_{1} ... v_{μ})$ is the basis. As an application, we calculate the $b$ -function of $f$ in the case of two variables.

On the topological triviality along moduli of deformations of $J_{k, 0}$ singularities

Piotr Jaworski (2000)

Annales Polonici Mathematici

It is well known that versal deformations of nonsimple singularities depend on moduli. However they can be topologically trivial along some or all of them. The first step in the investigation of this phenomenon is to determine the versal discriminant (unstable locus), which roughly speaking is the obstacle to analytic triviality. The next one is to construct continuous liftable vector fields smooth far from the versal discriminant and to integrate them. In this paper we extend the results of J....

On the topology of holomorphic foliations on Hopf manifolds

Daniel Mall (1993)

Compositio Mathematica

On the Torsion of Brieskorn Modules of Homogeneous Polynomials

Khurram Shabbir (2008)

Rendiconti del Seminario Matematico della Università di Padova

On the uniqueness of the quasihomogeneity

Piotr Jaworski (1999)

Banach Center Publications

The aim of this paper is to show that the quasihomogeneity of a quasihomogeneous germ with an isolated singularity uniquely extends to the base of its analytic miniversal deformation.

On the vanishing of local homotopy groups for isolated singularities of complex spaces.

Helmut A. Hamm (1981)

Journal für die reine und angewandte Mathematik

On the versal discriminant of $J_{k, 0}$ singularities

Piotr Jaworski (1996)

Annales Polonici Mathematici

It is well known that the versal deformations of nonsimple singularities depend on moduli. The first step in deeper understanding of this phenomenon is to determine the versal discriminant, which roughly speaking is an obstacle to analytic triviality of an unfolding or deformation along the moduli. The versal discriminant of the Pham singularity ( $J_{3, 0}$ in Arnold’s classification) was thoroughly investigated by J. Damon and A. Galligo [2], [3], [4]. The goal of this paper is to continue their work and...

On the Versal Resolutions of Deformations of Rational Double Points.

Frans Huikeshoven (1973)

Inventiones mathematicae

Currently displaying 61 – 80 of 88

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