LVMB manifolds and simplicial spheres
LVMB manifolds and simplicial spheres
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LVMB 流形和单纯球体
DOI：
10.5802/aif.2723
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
J'erome Tambour
中科院分区：
文献类型：
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作者：
J'erome Tambour
LVM和LVMB流形是非卡勒流形的一大类例子。例如，Hopf流形和Calabi-Eckmann流形可以被视为LVMB流形。左偏流形具有真实的环面的一个非常自然的作用，这个作用的商是一个简单的多面体。这个商使我们能够密切相关的LVM流形的矩角流形研究（例如）由布赫斯塔伯和帕诺夫。本文的目的是将与左偏流形相关的多面体推广到左偏流形，并研究其性质。特别是，我们表明，它属于一个非常大的类的单纯球。此外，我们表明，对于属于这个类的每一个领域，我们可以构建一个LMVB流形，其相关的领域是给定的领域。我们使用后者的结果表明，许多力矩角复合物可以赋予一个复杂的结构（产品与圆）。
LVM and LVMB manifolds are a large family of examples of non kahler 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).