On the degree of polar transformations. An approach through logarithmic foliations |
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Authors: | T Fassarella J V Pereira |
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Institution: | (1) IMPA Estrada Dona Castorina, 110 – Jardim Botanico, 22460-320 RJ, Brasil |
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Abstract: | 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.
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 14E05 37F75 |
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