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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 $$\mathbb {CP}^3$$ CP 3 can not exceed 94. We construct a real nonsingular sextic $$X$$ X in $$\mathbb {CP}^3$$ CP 3 satisfying $$b_1(\mathbb {R}X)=90$$ b 1 ( 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.
Mathematische Zeitschrift – Springer Journals
Published: May 20, 2015
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