Real cubic hypersurfaces and group laws.

Huisman, Johannes. "Real cubic hypersurfaces and group laws.." Revista Matemática Complutense 17.2 (2004): 395-401. <http://eudml.org/doc/44524>.

@article{Huisman2004,
abstract = {Let X be a real cubic hypersurface in Pn. Let C be the pseudo-hyperplane of X, i.e., C is the irreducible global real analytic branch of the real analytic variety X(R) such that the homology class [C] is nonzero in Hn-1(Pn(R),Z/2Z). Let L be the set of real linear subspaces L of Pn of dimension n - 2 contained in X such that L(R) ⊆ C. We show that, under certain conditions on X, there is a group law on the set L. It is determined by L + L' + L = 0 in L if and only if there is a real hyperplane H in Pn such that H · X = L + L' + L''. We also study the case when these conditions on X are not satisfied.},
author = {Huisman, Johannes},
journal = {Revista Matemática Complutense},
keywords = {Variedad algebraica; Hipersuperficies; Curvas cúbicas; Grupos; real cubic curve; pseudo-hyperplane},
language = {eng},
number = {2},
pages = {395-401},
title = {Real cubic hypersurfaces and group laws.},
url = {http://eudml.org/doc/44524},
volume = {17},
year = {2004},
}

TY - JOUR
AU - Huisman, Johannes
TI - Real cubic hypersurfaces and group laws.
JO - Revista Matemática Complutense
PY - 2004
VL - 17
IS - 2
SP - 395
EP - 401
AB - Let X be a real cubic hypersurface in Pn. Let C be the pseudo-hyperplane of X, i.e., C is the irreducible global real analytic branch of the real analytic variety X(R) such that the homology class [C] is nonzero in Hn-1(Pn(R),Z/2Z). Let L be the set of real linear subspaces L of Pn of dimension n - 2 contained in X such that L(R) ⊆ C. We show that, under certain conditions on X, there is a group law on the set L. It is determined by L + L' + L = 0 in L if and only if there is a real hyperplane H in Pn such that H · X = L + L' + L''. We also study the case when these conditions on X are not satisfied.
LA - eng
KW - Variedad algebraica; Hipersuperficies; Curvas cúbicas; Grupos; real cubic curve; pseudo-hyperplane
UR - http://eudml.org/doc/44524
ER -