| Construction Of Real Algebraic Plane Nodal Curves With Given Topology And Generically Optimal Degree I: the orientable case (2007) | |||||||||||||
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| We study a constructive method to find an algebraic curve in the real projective plane with a (possibly singular) topological type given in advance. Our method works if the topological model T to be realized has only double singularities. In that case, it gives an algebraic curve of degree 2N + 2K, where N and K are the numbers of double points and connected components of T . This bound is generically optimal and the topological models T for which the degree is optimal have a combinatorial characterization. The construction is based on a preliminar topological manipulation of the topological model followed by some perturbation techniques to obtain the polynomial defining the algebraic curve. This paper considers only the case in which T is orientable. The non-orientable case will appear in a separate paper. 1991 Mathematics Subject Classification: 14P25, 14Q05 1 Introduction In a previous paper by the author [Santos1] it is shown that any real algebraic plane nodal curve with N sin... | |||||||||||||
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