It follows from the known restrictions on the topology of a real algebraic variety that the number of handles of the real part of a real nonsingular sextic in CP3 is at most 47. We construct a real nonsingular sextic X6 in CP3 whose real part RX6 has 44 handles. In particular, this surface verifies b1(RX6) = h1,1(X6) + 2. We extend the construction in order to obtain for any even m ≥ 6 a real nonsingular surface Xm of degree m in CP3 verifying b1(RXm) > h1,1(Xm). It is known that such a surface does not exist if m ≤ 4.
@article{urn:eudml:doc:44387,
title = {Une sextique de l'espace projectif r\'eel avec un grand nombre d'anses.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {14},
year = {2001},
pages = {439-461},
zbl = {1073.14558},
mrnumber = {MR1871307},
language = {fr},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44387}
}
Bihan, Frédéric. Une sextique de l'espace projectif réel avec un grand nombre d'anses.. Revista Matemática de la Universidad Complutense de Madrid, Tome 14 (2001) pp. 439-461. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44387/