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Local intersections of plane algebraic curves
Author(s):
Claire
Moura
Journal:
Proc. Amer. Math. Soc.
132
(2004),
687-690.
MSC (2000):
Primary 14H50
Posted:
July 16, 2003
MathSciNet review:
2019943
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Abstract:
We determine the maximum punctual order of contact between two plane algebraic curves, of which one is reduced. We prove that, generically on the reduced curve, this quantity is always strictly bounded by the product of the degrees of the curves.
References:
- 1.
- A. Gabrielov, Multiplicities of zeroes of polynomials on trajectories of polynomial vector fields and bounds on degree of nonholonomy, Math. Res. Lett. 2 (1995), 437-451. MR 97c:14055
- 2.
- A. R. Magid, Lectures on differential Galois theory, University Lecture Series, volume 7, Amer. Math. Soc., Providence, RI, 1994. MR 95j:12008
- 3.
- R. Miranda, Algebraic curves and Riemann surfaces, Graduate Studies in Mathematics, volume 5, chapter 7, Amer. Math, Soc., Providence, RI, 1995. MR 96f:14029
- 4.
- Y. Yomdin, Oscillation of analytic curves, Proc. Amer. Math. Soc. 126, volume 2 (1998), 357-364. MR 98d:32033
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Additional Information:
Claire
Moura
Affiliation:
Laboratoire de Mathématiques E. Picard, Université Paul Sabatier, UFR MIG, 118 route de Narbonne, 31062 Toulouse Cedex 4, France - and - Departmento de Álgebra, Geometría y Topología, Facultad de Ciencias, 47005 Valladolid, Spain
Email:
moura@picard.ups-tlse.fr
DOI:
10.1090/S0002-9939-03-07178-8
PII:
S 0002-9939(03)07178-8
Received by editor(s):
January 16, 2001
Received by editor(s) in revised form:
November 5, 2002
Posted:
July 16, 2003
Additional Notes:
This work was partially supported by CNRS and EU contract ERBFMRXCT 960040 Valladolid (Spain).
Communicated by:
Michael Stillman
Copyright of article:
Copyright
2003,
American Mathematical Society
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