Geodesic
Examples of smooth compact toric varieties that are not quasitoric manifolds
Suyama, Yusuke1
1Department of Mathematics, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
Algebraic and Geometric Topology, Tome 14 (2014) no. 5, pp. 3097-3106
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We construct smooth compact toric varieties of complex dimension ≥ 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.

DOI : 10.2140/agt.2014.14.3097
Classification : 52B05, 14M25, 57S15
Keywords: fan, toric manifold, quasitoric manifold, Barnette sphere

Suyama, Yusuke  1

1 Department of Mathematics, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan 
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Suyama, Yusuke. Examples of smooth compact toric varieties that are not quasitoric manifolds. Algebraic and Geometric Topology, Tome 14 (2014) no. 5, pp. 3097-3106. doi: 10.2140/agt.2014.14.3097

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