Complex algebraic plane curves via the Poincaré¿Hopf formula, I: Parametric lines

• Autores: Maciej Borodzik, Henryk Zoladek
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 229, Nº 2, 2007, págs. 307-338
• Idioma: inglés
• DOI: 10.2140/pjm.2007.229.307
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• Resumen

  • We present a new and very eficient approach to study topology of algebraic curves in C2. It relies on using the Poincaré¿Hopf formula, applied to a suitable Hamiltonian vector field, to estimate the number of double points and the Milnor numbers of singular points of the curve and on considering finite-dimensional spaces of curves with given asymptotics at infinity. We apply this method to classification of parametric lines with one self-intersection.