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Scientific article
English

A Viro theorem without convexity hypothesis for trigonal curves

Published inInternational mathematics research notices, vol. 2006, no. 87604, p. 1-33
Publication date2006
Abstract

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.

Citation (ISO format)
BERTRAND, Benoît, BRUGALLÉ, Erwan. A Viro theorem without convexity hypothesis for trigonal curves. In: International mathematics research notices, 2006, vol. 2006, n° 87604, p. 1–33. doi: 10.1155/IMRN/2006/87604
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ISSN of the journal1073-7928
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