LVMB manifolds and simplicial spheres

Abstract : LVM and LVMB manifolds are a large family of examples of non kähler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a very natural action of the real torus and the quotient of this action is a simple polytope. This quotient allows us to relate closely LVM manifolds to the moment-angle manifolds studied (for example) by Buchstaber and Panov. The aim of this paper is to generalize the polytopes associated to LVM manifolds to the LVMB case and study its properties. In particular, we show that it belongs to a very large class of simplicial spheres. Moreover, we show that for every sphere belonging to this class, we can construct a LMVB 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).
Complete list of metadatas

Cited literature [16 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00487248
Contributor : Jérôme Tambour <>
Submitted on : Wednesday, December 1, 2010 - 6:16:39 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Wednesday, March 2, 2011 - 3:19:11 AM

Files

EnglishVersion3.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00487248, version 3
  • ARXIV : 1006.1797

Collections

Citation

Jérôme Tambour. LVMB manifolds and simplicial spheres. 2010. ⟨hal-00487248v3⟩

Share

Metrics

Record views

154

Files downloads

135