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

Abstract

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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.

How to cite

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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 -

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