A sextic in real projective space with a large number of handles.

Frédéric Bihan

Revista Matemática Complutense (2001)

  • Volume: 14, Issue: 2, page 439-461
  • ISSN: 1139-1138


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.

How to cite


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>.

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},

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 -

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.