A note on Bézout's theorem
We present a version of Bézout's theorem basing on the intersection theory in complex analytic geometry. Some applications for products of surfaces and curves are also given.
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Sławomir Rams, Piotr Tworzewski, Tadeusz Winiarski (2005)
Annales Polonici Mathematici
We present a version of Bézout's theorem basing on the intersection theory in complex analytic geometry. Some applications for products of surfaces and curves are also given.
John J. Wavrik (1975)
Mathematische Annalen
Pierre D. Milman (1978)
Mathematische Annalen
Jan Chmielowski (1976)
Studia Mathematica
T. Winiarski (1986)
Annales Polonici Mathematici
Vagn Lundsgaard Hansen (1980)
Journal für die reine und angewandte Mathematik
Siegfried Bosch (1977)
Mathematische Annalen
Ernst Peschl, Ludwig Reich (1971)
Monatshefte für Mathematik
Janusz Adamus, Hadi Seyedinejad (2013)
Annales Polonici Mathematici
We show that non-flatness of a morphism φ:X→ Y of complex-analytic spaces with a locally irreducible target of dimension n manifests in the existence of vertical components in the n-fold fibred power of the pull-back of φ to the desingularization of Y. An algebraic analogue follows: Let R be a locally (analytically) irreducible finite type ℂ-algebra and an integral domain of Krull dimension n, and let S be a regular n-dimensional algebra of finite type over R (but not necessarily a finite R-module),...
S. Dimiev (1991)
Annales Polonici Mathematici
We study coherent subsheaves 𝓓 of the holomorphic tangent sheaf of a complex manifold. A description of the corresponding 𝓓-stable ideals and their closed complex subspaces is sketched. Our study of non-holonomicity is based on the Noetherian property of coherent analytic sheaves. This is inspired by the paper [3] which is related with some problems of mechanics.
Felipe Cano, Jean-François Mattei (1992)
Annales de l'institut Fourier
Soit un germe en de 1-forme différentielle holomorphe, satisfaisant la condition d’intégrabilité et non dicritique, i.e. sur toute surface non intégrale de , on ne peut tracer, au voisinage de 0, qu’un nombre fini de germes de courbes analytiques , intégrales de , avec . Alors possède un germe d’hypersurface analytique intégrale.
Le Van Thanh (1982)
Annales de l'institut Fourier
On donne des évaluations précises de la croissance modérée des intégrales de fonctions de classe de Nilsson locale dans , exprimées par des caractéristiques topologiques des courbes de ramification des intégrands.
Michael Freeman (1974)
Mathematische Annalen
Agler, Jim, McCarthy, John E., Stankus, Mark (2008)
The New York Journal of Mathematics [electronic only]
I.B. Penkov (1983)
Inventiones mathematicae
Arkadiusz Płoski (1988)
Banach Center Publications
Didier D'Acunto, Vincent Grandjean (2005)
Annales Polonici Mathematici
Let f: ℝⁿ → ℝ be a C² semialgebraic function and let c be an asymptotic critical value of f. We prove that there exists a smallest rational number such that |x|·|∇f| and are separated at infinity. If c is a regular value and , then f is a locally trivial fibration over c, and the trivialisation is realised by the flow of the gradient field of f.
Douglas, Ronald G., Misra, Gadadhar (2005)
The New York Journal of Mathematics [electronic only]
Jacek Chądzyński, Tadeusz Krasiński (1998)
Banach Center Publications
An effective formula for the Łojasiewicz exponent for analytic curves in a neighbourhood of 0 ∈ ℂ is given.
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 holds near 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.
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