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Indices of 1-forms and Newton polyhedra.

Alexander Esterov (2005)

Revista Matemática Complutense

A formula of Matsuo Oka (1990) expresses the Milnor number of a germ of a complex analytic map with a generic principal part in terms of the Newton polyhedra of the components of the map. In this paper this formula is generalized to the case of the index of a 1-form on a local complete intersection singularity (Theorem 1.10, Corollaries 1.11, 4.1). In particular, the Newton polyhedron of a 1-form is defined (Definition 1.6). This also simplifies the Oka formula in some particular cases (Propositions...

Inégalités de Łojasiewicz globales

Jean-Claude Tougeron (1991)

Annales de l'institut Fourier

On étudie les propriétés métriques des ensembles analytique réels f = 0 , avec f ∈ 𝒪 ( Ω ) , 𝒪 ( Ω ) algèbre analytique topologiquement noethérienne. Ainsi, on construit de larges classes d’algèbres 𝒪 ( Ω ) topologiquement noethériennes et vérifiant des conditions de Łojasiewicz globales d’un certain type. Comme application, on obtient des théorèmes de division de fonction 𝒞 ∞ par des fonctions analytiques.

Infinite geodesic rays in the space of Kähler potentials

Claudio Arezzo, Gang Tian (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper we prove the existence of solutions of a degenerate complex Monge-Ampére equation on a complex manifold. Applying our existence result to a special degeneration of complex structure, we show how to associate to a change of complex structure an infinite length geodetic ray in the space of potentials. We also prove an existence result for the initial value problem for geodesics. We end this paper with a discussion of a list of open problems indicating how to relate our reults to the...

Infinite-dimensional complex projective spaces and complete intersections

Edoardo Ballico (2006)

Mathematica Bohemica

Let V be an infinite-dimensional complex Banach space and X ⊂ 𝐏 ( V ) a closed analytic subset with finite codimension. We give a condition on X which implies that X is a complete intersection. We conjecture that the result should be true for more general topological vector spaces.

Infinitesimal automorphisms and deformations of parabolic geometries

Andreas Čap (2008)

Journal of the European Mathematical Society

We show that infinitesimal automorphisms and infinitesimal deformations of parabolic geometries can be nicely described in terms of the twisted de Rham sequence associated to a certain linear connection on the adjoint tractor bundle. For regular normal geometries, this description can be related to the underlying geometric structure using the machinery of BGG sequences. In the locally flat case, this leads to a deformation complex, which generalizes the well known complex for locally conformally...

Infinitesimal CR automorphisms for a class of polynomial models

Martin Kolář, Francine Meylan (2017)

Archivum Mathematicum

In this paper we study infinitesimal CR automorphisms of Levi degenerate hypersurfaces. We illustrate the recent general results of [18], [17], [15], on a class of concrete examples, polynomial models in ℂ 3 of the form ℑ w = ℜ ( P ( z ) Q ( z ) ¯ ) , where P and Q are weighted homogeneous holomorphic polynomials in z = ( z 1 , z 2 ) . We classify such models according to their Lie algebra of infinitesimal CR automorphisms. We also give the first example of a non monomial model which admits a nonlinear rigid automorphism.

Infinitesimal CR automorphisms of hypersurfaces of finite type in ℂ 2

Martin Kolář, Francine Meylan (2011)

Archivum Mathematicum

We study the Chern-Moser operator for hypersurfaces of finite type in ℂ 2 . Analysing its kernel, we derive explicit results on jet determination for the stability group, and give a description of infinitesimal CR automorphisms of such manifolds.

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