A Viro Theorem without convexity hypothesis for trigonal curves

Details A Viro Theorem without convexity hypothesis for trigonal curves A Viro Theorem without convexity hypothesis for trigonal curves

2006-02-09

arxiv.org/abs/math/0602198v2

Mathematics

Algebraic Geometry

26 pages, 18 figures

Scientific paper

A cumbersome hypothesis for Viro patchworking of real algebraic curves is the convexity of the given subdivision. It is an open question in general to know whether the convexity is necessary. In the case of trigonal curves we interpret Viro method in terms of dessins d'enfants. Gluing the dessins d'enfants in a coherent way we prove that no convexity hypothesis is required to patchwork such curves.

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