Tohoku Mathematical Journal
2016
March
SECOND SERIES VOL. 68, NO. 1

Tohoku Math. J.
68 (2016), 91-138

Title WEDGE OPERATIONS AND TORUS SYMMETRIES

Author Suyoung Choi and Hanchul Park

(Received February 12, 2014, revised August 27, 2014)
Abstract. A fundamental result of toric geometry is that there is a bijection between toric varieties and fans. More generally, it is known that some classes of manifolds having well-behaved torus actions, say toric objects, can be classified in terms of combinatorial data containing simplicial complexes.
  In this paper, we investigate the relationship between the topological toric manifolds over a simplicial complex $K$ and those over the complex obtained by simplicial wedge operations from $K$. Our result provides a systematic way to classify toric objects associated with the class of simplicial complexes obtained from a given $K$ by wedge operations. As applications, we completely classify smooth toric varieties with a few generators and show their projectivity. We also study smooth real toric varieties.

Mathematics Subject Classification. Primary 14M25; Secondary 52B20, 52B35.
Key words and phrases. Toric variety, projective toric variety, Gale diagram, simplicial wedge, topological toric manifold, real topological toric manifold, quasitoric manifold, small cover, real toric variety.

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