The Classical Bezout Theorem

1999 ◽  
pp. 7-42
Author(s):  
Hubert Flenner ◽  
Liam O’Carroll ◽  
Wolfgang Vogel
Keyword(s):  
Bezout Theorem

On the Bezout Theorem

2001 ◽  
pp. 695-714
Author(s):  
Kuo-Tsai Chen
Keyword(s):  
Bezout Theorem

scholarly journals Rational cuspidal curves in projective surfaces. Topological versus algebraic obstructions

2017 ◽  
Vol 28 (14) ◽  
pp. 1750106
Author(s):  
Maciej Borodzik
Keyword(s):  
Floer Homology ◽  
Singular Points ◽  
The Other ◽  
Heegaard Floer Homology ◽  
Heegaard Floer ◽  
Bezout Theorem ◽  
Projective Surfaces

We study rational cuspidal curves in projective surfaces. We specify two criteria obstructing possible configurations of singular points that may occur on such curves. One criterion generalizes the result of Fernandez de Bobadilla, Luengo, Melle–Hernandez and Némethi and is based on the Bézout theorem. The other one is a generalization of the result obtained by Livingston and the author and relies on Ozsváth–Szabó inequalities for [Formula: see text]-invariants in Heegaard Floer homology. We show by means of explicit calculations that the two approaches give very similar obstructions.

Newton polytopes and the Bezout theorem

1977 ◽  
Vol 10 (3) ◽  
pp. 233-235 ◽  
Author(s):  
A. G. Kushnirenko
Keyword(s):  
Newton Polytopes ◽  
Bezout Theorem

A COMMENT ON A NONIDEAL CENTRIFUGAL VIBRATOR MACHINE BEHAVIOR WITH SOFT AND HARD SPRINGS

2006 ◽  
Vol 16 (04) ◽  
pp. 1083-1088 ◽  
Author(s):  
MÁRCIO JOSÉ HORTA DANTAS ◽  
JOSÉ MANOEL BALTHAZAR
Keyword(s):  
Mechanical System ◽  
Classical Result ◽  
Chaotic Behavior ◽  
Damping Coefficient ◽  
Plane Curves ◽  
Center Manifolds ◽  
Nonlinear Spring ◽  
Homoclinic Chaos ◽  
Rotating Machine ◽  
Bezout Theorem

This paper concerns a type of rotating machine (centrifugal vibrator), which is supported on a nonlinear spring. This is a nonideal kind of mechanical system. The goal of the present work is to show the striking differences between the cases where we take into account soft and hard spring types. For soft spring, we prove the existence of homoclinic chaos. By using the Melnikov's Method, we show the existence of an interval with the following property: if a certain parameter belongs to this interval, then we have chaotic behavior; otherwise, this does not happen. Furthermore, if we use an appropriate damping coefficient, the chaotic behavior can be avoided. For hard spring, we prove the existence of Hopf's Bifurcation, by using reduction to Center Manifolds and the Bezout Theorem (a classical result about algebraic plane curves).

scholarly journals Local Bézout theorem for Henselian rings

2016 ◽  
Vol 68 (3) ◽  
pp. 419-432
Author(s):  
M. Emilia Alonso ◽  
Henri Lombardi
Keyword(s):  
Bezout Theorem

scholarly journals Nonproper intersection products and generalized cycles

2021 ◽  
Author(s):  
Mats Andersson ◽  
Dennis Eriksson ◽  
Håkan Samuelsson Kalm ◽  
Elizabeth Wulcan ◽  
Alain Yger
Keyword(s):  
Projective Space ◽  
Chow Group ◽  
Intersection Theory ◽  
Analytic Space ◽  
Intersection Numbers ◽  
Formula Group ◽  
Bezout Theorem ◽  
Join Construction ◽  
Chern Forms

AbstractWe develop intersection theory in terms of the $${{\mathscr {B}}}$$ B -group of a reduced analytic space. This group was introduced in a previous work as an analogue of the Chow group; it is generated by currents that are direct images of Chern forms and it contains all usual cycles. However, contrary to Chow classes, the $${{\mathscr {B}}}$$ B -classes have well-defined multiplicities at each point. We focus on a $${{\mathscr {B}}}$$ B -analogue of the intersection theory based on the Stückrad–Vogel procedure and the join construction in projective space. Our approach provides global $${{\mathscr {B}}}$$ B -classes which satisfy a Bézout theorem and have the expected local intersection numbers. We also introduce $${{\mathscr {B}}}$$ B -analogues of more classical constructions of intersections using the Gysin map of the diagonal. These constructions are connected via a $${{\mathscr {B}}}$$ B -variant of van Gastel’s formulas. Furthermore, we prove that our intersections coincide with the classical ones on cohomology level.

scholarly journals Local Bézout Theorem

2010 ◽  
Vol 45 (10) ◽  
pp. 975-985 ◽  
Author(s):  
M. Emilia Alonso ◽  
Henri Lombardi
Keyword(s):  
Bezout Theorem
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