#### Volume 14, issue 5 (2014)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
Examples of smooth compact toric varieties that are not quasitoric manifolds

### Yusuke Suyama

Algebraic & Geometric Topology 14 (2014) 3097–3106
##### Abstract

We construct smooth compact toric varieties of complex dimension $\ge 4$ whose orbit spaces by the action of the compact torus are not homeomorphic to simple polytopes (as manifolds with corners). These provide the first known examples of smooth compact toric varieties that are not quasitoric manifolds.

##### Keywords
fan, toric manifold, quasitoric manifold, Barnette sphere
##### Mathematical Subject Classification 2010
Primary: 52B05
Secondary: 14M25, 57S15