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/lp/de-gruyter/criteria-for-hattori-masuda-multi-polytopes-via-duistermaat-heckman-Bz0DmxZg4g
- Publisher
- de Gruyter
- Copyright
- © 2018 Walter de Gruyter GmbH, Berlin/Boston
- ISSN
- 1615-7168
- eISSN
- 1615-7168
- DOI
- 10.1515/advgeom-2017-0023
- Publisher site
- See Article on Publisher Site
Abstract
AbstractA multi-fan (respectively multi-polytope), introduced first by Hattori and Masuda, is a purely combinatorial object generalizing an ordinary fan (respectively polytope) in algebraic geometry. It is well known that an ordinary fan or polytope is associated with a toric variety. On the other hand, we can geometrically realize multi-fans in terms of torus manifolds. However, it is unfortunate that two different torus manifolds may correspond to the same multi-fan. The goal of this paper is to give some criteria for a multi-polytope to be an ordinary polytope in terms of the Duistermaat–Heckman functions and winding numbers. Moreover, we also prove a generalized Pick formula and its consequences for simple lattice multi-polytopes by studying their Ehrhart polynomials.
Journal
Advances in Geometry – de Gruyter
Published: Jul 26, 2018