Examples of smooth compact toric varieties that are not quasitoric manifolds

Suyama, Yusuke

doi:10.2140/agt.2014.14.3097

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Examples of smooth compact toric varieties that are not quasitoric manifolds

Yusuke Suyama

Algebraic & Geometric Topology 14 (2014) 3097–3106

DOI: 10.2140/agt.2014.14.3097

Abstract

We construct smooth compact toric varieties of complex dimension $\geq 4$ 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

References

Publication

Received: 23 December 2013

Revised: 19 April 2014

Accepted: 24 April 2014

Published: 5 November 2014

Authors

Yusuke Suyama
Department of Mathematics Osaka City University 3-3-138 Sugimoto Sumiyoshi-ku Osaka 558-8585 Japan

Volume 14, issue 5 (2014)