Local intersections of plane algebraic curves
HTML articles powered by AMS MathViewer
- by Claire Moura PDF
- Proc. Amer. Math. Soc. 132 (2004), 687-690 Request permission
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
- Andrei Gabrielov, Multiplicities of zeroes of polynomials on trajectories of polynomial vector fields and bounds on degree of nonholonomy, Math. Res. Lett. 2 (1995), no. 4, 437–451. MR 1355706, DOI 10.4310/MRL.1995.v2.n4.a5
- Andy R. Magid, Lectures on differential Galois theory, University Lecture Series, vol. 7, American Mathematical Society, Providence, RI, 1994. MR 1301076, DOI 10.1090/ulect/007
- Rick Miranda, Algebraic curves and Riemann surfaces, Graduate Studies in Mathematics, vol. 5, American Mathematical Society, Providence, RI, 1995. MR 1326604, DOI 10.1090/gsm/005
- Y. Yomdin, Oscillation of analytic curves, Proc. Amer. Math. Soc. 126 (1998), no. 2, 357–364. MR 1443861, DOI 10.1090/S0002-9939-98-04265-8
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
- Received by editor(s): January 16, 2001
- Received by editor(s) in revised form: November 5, 2002
- Published electronically: July 16, 2003
- Additional Notes: This work was partially supported by CNRS and EU contract ERBFMRXCT 960040 Valladolid (Spain).
- Communicated by: Michael Stillman
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 687-690
- MSC (2000): Primary 14H50
- DOI: https://doi.org/10.1090/S0002-9939-03-07178-8
- MathSciNet review: 2019943