Polar germs and singularity invariants

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hdl:2099.1/25313
Document typeMaster thesis
Date2009-07
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Abstract
In this work we obtain an algorithm which explicitly recovers the cluster of singular points a germ of curve from the cluster of base points of the polar germs of the curve. To achieve this, we reinterpret the problem in terms of the recently developed theory of planar analytic morphisms. The result is a sort of local version of the known fact in projective geometry that the proper singular points of a plane projective algebraic curve are exactly the proper base points of its polar curves.. L'objectiu és revisar resultats clàssics de gèrmens polars de corba plana des de la nova perspectiva del desenvolupament recent de la teoria de morfismes analítics entre superfícies no singulars. Aquesta teoria ha estat desenvolupada des del punt de vista geomètric per Casas i des del punt de vista algebraic, a través de la teoria de valoracions, per Favre i Jonsson. S'estudiaran els dos punts de vista i s'intentaran aplicar a la teoria de polars.
DegreeMÀSTER UNIVERSITARI EN MATEMÀTICA APLICADA (Pla 2009)
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