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

Abstract

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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).

How to cite

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Tambour, 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 -

References

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