On the degree of polar transformations. An approach through logarithmic foliations

• T. Fassarella ^[1] ; J. V. Pereira ^[1]
  1. [1] Instituto Nacional de Matemática Pura e Aplicada

     Instituto Nacional de Matemática Pura e Aplicada

     Brasil

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 13, Nº. 2, 2007, págs. 239-252
• Idioma: inglés
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• Resumen

  • We investigate the degree of the polar transformations associated to a certain class of multi-valued homogeneous functions. In particular we prove that the degree of the preimage of generic linear spaces by a polar transformation associated to a homogeneous polynomial F is determined by the zero locus of F. For zero dimensional-dimensional linear spaces this was conjectured by Dolgachev and proved by Dimca–Papadima using topological arguments. Our methods are algebro-geometric and rely on the study of the Gauss map of naturally associated logarithmic foliations.