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arXiv · 1412.4212

A real sextic surface with 45 handles

Arthur Renaudineau
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Abstract

It follows from classical restrictions on the topology of real algebraic varieties that the first Betti number of the real part of a real nonsingular sextic in $\mathbb{CP}^3$ can not exceed $94$. We construct a real nonsingular sextic $X$ in $\mathbb{CP}^3$ satisfying $b_1(\mathbb{R}X)=90$, improving a result of F.Bihan. The construction uses Viro's patchworking and an equivariant version of a deformation due to E.Horikawa.

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Arthur Renaudineau. 2014-12-13. A real sextic surface with 45 handles. https://arxiv.org/abs/1412.4212

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