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

@article{citeulike:2371586, abstract = {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.}, author = {Fassarella, T. and Pereira, J.}, citeulike-article-id = {2371586}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/s00029-007-0040-x}, day = {24}, doi = {10.1007/s00029-007-0040-x}, journal = {Selecta Mathematica, New Series}, keywords = {complex\_analysis, fewnomials, foliations}, number = {2}, pages = {239--252}, posted-at = {2008-02-13 21:10:32}, priority = {3}, title = {On the degree of polar transformations. An approach through logarithmic foliations}, url = {http://dx.doi.org/10.1007/s00029-007-0040-x}, volume = {13}, year = {2007} }

TY - JOUR ID - citeulike:2371586 L3 - citeulike-article-id:2371586 N2 - 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. IS - 2 JF - Selecta Mathematica, New Series EP - 252 TI - On the degree of polar transformations. An approach through logarithmic foliations VL - 13 SP - 239 KW - complex_analysis KW - fewnomials KW - foliations AU - Fassarella, T AU - Pereira, J PY - 2007//24/ UR - http://dx.doi.org/10.1007/s00029-007-0040-x ER -