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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.
Bihan, Frédéric. "Une sextique de l'espace projectif réel avec un grand nombre d'anses.." Revista Matemática Complutense 14.2 (2001): 439-461. <http://eudml.org/doc/44387>.
@article{Bihan2001, author = {Bihan, Frédéric}, journal = {Revista Matemática Complutense}, keywords = {Geometría algebraica; Espacio proyectivo; Superficies algebraicas}, language = {fre}, number = {2}, pages = {439-461}, title = {Une sextique de l'espace projectif réel avec un grand nombre d'anses.}, url = {http://eudml.org/doc/44387}, volume = {14}, year = {2001}, }
TY - JOUR AU - Bihan, Frédéric TI - Une sextique de l'espace projectif réel avec un grand nombre d'anses. JO - Revista Matemática Complutense PY - 2001 VL - 14 IS - 2 SP - 439 EP - 461 LA - fre KW - Geometría algebraica; Espacio proyectivo; Superficies algebraicas UR - http://eudml.org/doc/44387 ER -