# LVMB manifolds and simplicial spheres

Jérôme Tambour^{[1]}

- [1] Université de Bourgogne Institut de Mathématiques de Bourgogne 9 Av. Alain Savary 21078 Dijon Cedex France

Annales de l’institut Fourier (2012)

- Volume: 62, Issue: 4, page 1289-1317
- ISSN: 0373-0956

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topTambour, Jérôme. "LVMB manifolds and simplicial spheres." Annales de l’institut Fourier 62.4 (2012): 1289-1317. <http://eudml.org/doc/251094>.

@article{Tambour2012,

abstract = {LVM and LVMB manifolds are a large family of non kähler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a natural action of a real torus and the quotient of this action is a polytope. This quotient allows us to relate closely LVM manifolds to the moment-angle manifolds studied by Buchstaber and Panov. Our aim is to generalize the polytope associated to a LVM manifold to the LVMB case and study the properties of this generalization. In particular, we show that the object we obtain belongs to a very large class of simplicial spheres. Moreover, we show that for every sphere belonging to this class, we can construct a LVMB manifold whose associated sphere is the given sphere. We use this latter result to show that many moment-angle complexes can be endowed with a complex structure (up to product with circles).},

affiliation = {Université de Bourgogne Institut de Mathématiques de Bourgogne 9 Av. Alain Savary 21078 Dijon Cedex France},

author = {Tambour, Jérôme},

journal = {Annales de l’institut Fourier},

keywords = {non Kähler compact complex manifolds; simplicial spheres; toric varieties; complex structure on some moment-angle complexes; Lopez de Medrano-Verjovsky-Meersseman (LVM); Lopez de Medrano-Verjovsky-Meersseman-Bosio (LVMB)},

language = {eng},

number = {4},

pages = {1289-1317},

publisher = {Association des Annales de l’institut Fourier},

title = {LVMB manifolds and simplicial spheres},

url = {http://eudml.org/doc/251094},

volume = {62},

year = {2012},

}

TY - JOUR

AU - Tambour, Jérôme

TI - LVMB manifolds and simplicial spheres

JO - Annales de l’institut Fourier

PY - 2012

PB - Association des Annales de l’institut Fourier

VL - 62

IS - 4

SP - 1289

EP - 1317

AB - LVM and LVMB manifolds are a large family of non kähler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a natural action of a real torus and the quotient of this action is a polytope. This quotient allows us to relate closely LVM manifolds to the moment-angle manifolds studied by Buchstaber and Panov. Our aim is to generalize the polytope associated to a LVM manifold to the LVMB case and study the properties of this generalization. In particular, we show that the object we obtain belongs to a very large class of simplicial spheres. Moreover, we show that for every sphere belonging to this class, we can construct a LVMB manifold whose associated sphere is the given sphere. We use this latter result to show that many moment-angle complexes can be endowed with a complex structure (up to product with circles).

LA - eng

KW - non Kähler compact complex manifolds; simplicial spheres; toric varieties; complex structure on some moment-angle complexes; Lopez de Medrano-Verjovsky-Meersseman (LVM); Lopez de Medrano-Verjovsky-Meersseman-Bosio (LVMB)

UR - http://eudml.org/doc/251094

ER -

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