Geodesic
Classification Problem for Quasitoric Manifolds over a Given Simple Polytope
Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 2, pp. 3-11 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The classification problem for quasitoric manifolds over a given polytope $P^n$ is considered. The known construction of weights, which was used in the study of the similar problem for toric manifolds, is modified. The construction thus obtained is applied to the solution of the above problem in small dimensions. Classification results are also obtained for polytopes that are products of finitely many simplices of arbitrary dimensions. 
@article{FAA_2001_35_2_a0,
     author = {N. E. Dobrinskaya},
     title = {Classification {Problem} for {Quasitoric} {Manifolds} over a {Given} {Simple} {Polytope}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {3--11},
     year = {2001},
     volume = {35},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2001_35_2_a0/}
}
TY  - JOUR
AU  - N. E. Dobrinskaya
TI  - Classification Problem for Quasitoric Manifolds over a Given Simple Polytope
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2001
SP  - 3
EP  - 11
VL  - 35
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/FAA_2001_35_2_a0/
LA  - ru
ID  - FAA_2001_35_2_a0
ER  - 
%0 Journal Article
%A N. E. Dobrinskaya
%T Classification Problem for Quasitoric Manifolds over a Given Simple Polytope
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2001
%P 3-11
%V 35
%N 2
%U http://geodesic.mathdoc.fr/item/FAA_2001_35_2_a0/
%G ru
%F FAA_2001_35_2_a0
N. E. Dobrinskaya. Classification Problem for Quasitoric Manifolds over a Given Simple Polytope. Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 2, pp. 3-11. http://geodesic.mathdoc.fr/item/FAA_2001_35_2_a0/

[1] Bukhshtaber V. M., Rai N., “Toricheskie mnogoobraziya i kompleksnye kobordizmy”, UMN, 53:2 (1998), 139–141 | DOI | MR

[2] Davis M., “Smooth $G$-manifolds as collection of fiber bundles”, Pacific J. Math., 77:2 (1978), 315–363 | DOI | MR | Zbl

[3] Davis M., Januszkiewicz T., “Convex polytopes, Coxeter orbifolds and torus actions”, Duke Math. J., 62:2 (1991), 417–451 | DOI | MR | Zbl

[4] Kleinschmidt P., “A classification of toric varieties with few generators”, Aequationes Math., 35:2–3 (1988), 254–266 | DOI | MR | Zbl

[5] Oda T., “Convex bodies and algebraic geometry. An introduction to the theory of toric varieties”, Ergeb. Math. Grenzgeb. (3), 15, Springer-Verlag, Berlin, 1988 | MR

[6] Orlik P., Raymond F., “Actions of the torus on $4$-manifolds”, Trans. Amer. Math. Soc., 152 (1970), 531–559 | DOI | MR | Zbl