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Non oscillating solutions of analytic gradient vector fields

Fernando Sanz (1998)

Annales de l'institut Fourier

Let γ be an integral solution of an analytic real vector field ξ defined in a neighbordhood of 0 ∈ ℝ 3 . Suppose that γ has a single limit point, ω ( γ ) = { 0 } . We say that γ is non oscillating if, for any analytic surface H , either γ is contained in H or γ cuts H only finitely many times. In this paper we give a sufficient condition for γ to be non oscillating. It is established in terms of the existence of “generalized iterated tangents”, i.e. the existence of a single limit point for any transform property for...

Non-embeddable 1 -convex manifolds

Jan Stevens (2014)

Annales de l’institut Fourier

We show that every small resolution of a 3-dimensional terminal hypersurface singularity can occur on a non-embeddable 1 -convex manifold.We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve with normal bundle of type ( 1 , - 3 ) . To this end we study small resolutions of c D 4 -singularities.

On Bochner-Martinelli residue currents and their annihilator ideals

Mattias Jonsson, Elizabeth Wulcan (2009)

Annales de l’institut Fourier

We study the residue current R f of Bochner-Martinelli type associated with a tuple f = ( f 1 , ⋯ , f m ) of holomorphic germs at 0 ∈ 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 ) .

On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold

Zhiwei Wang (2016)

Annales Polonici Mathematici

This paper divides into two parts. Let (X,ω) be a compact Hermitian manifold. Firstly, if the Hermitian metric ω satisfies the assumption that ∂ ∂ ̅ ω k = 0 for all k, we generalize the volume of the cohomology class in the Kähler setting to the Hermitian setting, and prove that the volume is always finite and the Grauert-Riemenschneider type criterion holds true, which is a partial answer to a conjecture posed by Boucksom. Secondly, we observe that if the anticanonical bundle K X - 1 is nef, then for any ε >...

Quantifier elimination in quasianalytic structures via non-standard analysis

Krzysztof Jan Nowak (2015)

Annales Polonici Mathematici

The paper is a continuation of an earlier one where we developed a theory of active and non-active infinitesimals and intended to establish quantifier elimination in quasianalytic structures. That article, however, did not attain full generality, which refers to one of its results, namely the theorem on an active infinitesimal, playing an essential role in our non-standard analysis. The general case was covered in our subsequent preprint, which constitutes a basis for the approach presented here....

Quantifier elimination, valuation property and preparation theorem in quasianalytic geometry via transformation to normal crossings

Krzysztof Jan Nowak (2009)

Annales Polonici Mathematici

This paper investigates the geometry of the expansion Q of the real field ℝ by restricted quasianalytic functions. The main purpose is to establish quantifier elimination, description of definable functions by terms, the valuation property and preparation theorem (in the sense of Parusiński-Lion-Rolin). To this end, we study non-standard models of the universal diagram T of Q in the language ℒ augmented by the names of rational powers. Our approach makes no appeal to the Weierstrass preparation...

Currently displaying 41 – 60 of 88