# Publications

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## A Viro Theorem without convexity hypothesis for trigonal curves

### (Joint with B. Bertrand)

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.