# Real cubic hypersurfaces and group laws.

Revista Matemática Complutense (2004)

- Volume: 17, Issue: 2, page 395-401
- ISSN: 1139-1138

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topHuisman, 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 -

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