Let X be the three-dimensional, complete, nonsingular, complex torus embedding corresponding to a fan and let V be the real part of X (for definitions see [1] or [3]). The aim of this note is to give a simple combinatorial formula for calculating the Betti numbers of V.
@article{bwmeta1.element.bwnjournal-article-cmv64i1p59bwm,
author = {Jan Ratajski},
title = {On the Betti numbers of the real part of a three-dimensional torus embedding},
journal = {Colloquium Mathematicae},
volume = {66},
year = {1993},
pages = {59-64},
zbl = {0851.57027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv64i1p59bwm}
}
Ratajski, Jan. On the Betti numbers of the real part of a three-dimensional torus embedding. Colloquium Mathematicae, Tome 66 (1993) pp. 59-64. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv64i1p59bwm/
[000] [1] J. Jurkiewicz, Torus embeddings, polyhedra, k*-actions and homology, Dissertationes Math. 236 (1985). | Zbl 0599.14014
[001] [2] G. Kempf, F. Knudsen, D. Mumford and B. Saint-Donat, Toroidal Embeddings I, Lecture Notes in Math. 339, Springer, 1973. | Zbl 0271.14017
[002] [3] T. Oda, Convex Bodies and Algebraic Geometry, Springer, 1980.
[003] [4] J. Stillwell, Classical Topology and Combinatorial Group Theory, Springer, 1980.