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A real sextic surface with 45 handles

A real sextic surface with 45 handles 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

A real sextic surface with 45 handles

Mathematische Zeitschrift , Volume 281 (2) – May 20, 2015

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References (15)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/s00209-015-1482-z
Publisher site
See Article on Publisher Site

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 $$\mathbb {CP}^3$$ 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.

Journal

Mathematische ZeitschriftSpringer Journals

Published: May 20, 2015

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