Patchworking singular algebraic curves I |
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Authors: | Eugenii Shustin Ilya Tyomkin |
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Affiliation: | (1) School of Mathematical Sciences, Tel Aviv University Ramat Aviv, 69978 Tel Aviv, Israel;(2) Institut de Mathématiques, Algèbres d'opérateurs et répresentations, Université Pierre et Marie Curie, 175 rue du Chevaleret, plateu 7D, F-75013 Paris, France |
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Abstract: | In this paper we present a general patchworking procedure for the construction of reduced singular curves having prescribed singularities and belonging to a given linear system on algebraic surfaces. It originates in the Viro “gluing” method for the construction of real non-singular algebraic hypersurfaces. The general procedure includes almost all known particular modifications, and goes far beyond. Some applications and examples illustrate the construction. Both authors were partially supported by the Herman Minkowsky-Minerva Center for Geometry at Tel Aviv University, and by grant no. G-616-15.6/99 from the German-Israeli Foundation for Research and Development. The first author was also supported by the Bessel Research Award from the Alexander von Humboldt Foundation. The second author was also partially supported by the EC-network ‘Algebraic Lie Representations” contract no. ERB-FMRX-CT97-0100. |
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