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A real sextic surface with 45 handles

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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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Acknowledgments

I am very grateful to Erwan Brugallé and Ilia Itenberg for useful discussions and advisements. I thank also the unknown referee for useful comments on a preliminary version of this paper.

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  1. Université Pierre et Marie Curie, Institut de Mathématiques de Jussieu-Paris Rive Gauche, 4 place Jussieu, Case 247 75252, Paris, Cedex 5, France

    Arthur Renaudineau

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  1. Arthur Renaudineau
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Correspondence to Arthur Renaudineau.

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Renaudineau, A. A real sextic surface with 45 handles. Math. Z. 281, 241–256 (2015). https://doi.org/10.1007/s00209-015-1482-z

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