We establish a correspondence between simplicial fans, not necessarily rational, and certain foliated compact complex manifolds called LVMB-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 two. 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.

Foliations Modelling Nonrational Simplicial Toric Varieties / Fiammetta Battaglia; Dan Zaffran. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - STAMPA. - 2015:(2015), pp. 11785-11815. [10.1093/imrn/rnv035]

Foliations Modelling Nonrational Simplicial Toric Varieties

BATTAGLIA, FIAMMETTA;
2015

Abstract

We establish a correspondence between simplicial fans, not necessarily rational, and certain foliated compact complex manifolds called LVMB-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 two. 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.
2015
2015
11785
11815
Fiammetta Battaglia; Dan Zaffran
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/965787
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