Foliations Modeling Nonrational Simplicial Toric Varieties

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We establish a correspondence between simplicial fans, not necessarily rational, and certain foliated compact complex manifolds called LVMB-manifolds (named after Lopez de Medrano, Verjovsky, Meersseman, Bosio-manifolds). In the rational case, Meersseman and Verjovsky have shown that the leaf space is the usual toric variety. We compute the basic Betti numbers of the foliation for shellable fans. When the fan is in particular polytopal, we prove that the basic cohomology of the foliation is generated in degree 2. We give evidence that the rich interplay between convex and algebraic geometries embodied by toric varieties carries over to our nonrational construction. In fact, our approach unifies rational and nonrational cases.
Publisher
OXFORD UNIV PRESS
Issue Date
2015
Language
English
Article Type
Article
Keywords

COMPACT COMPLEX-MANIFOLDS; CONVEX POLYTOPES; RIEMANNIAN FOLIATION; TORUS ACTIONS; CONSTRUCTION; ORBIFOLDS; GEOMETRY; STACKS; NUMBER

Citation

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, no.22, pp.11785 - 11815

ISSN
1073-7928
DOI
10.1093/imrn/rnv035
URI
http://hdl.handle.net/10203/205757
Appears in Collection
MA-Journal Papers(저널논문)
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