Volume 14, issue 5 (2014)

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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