Bott towers, crosspolytopes and torus actions

Civan Y.

GEOMETRIAE DEDICATA, vol.113, no.1, pp.55-74, 2005 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 113 Issue: 1
  • Publication Date: 2005
  • Doi Number: 10.1007/s10711-005-1725-y
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.55-74
  • Süleyman Demirel University Affiliated: Yes


We study the geometry and topology of Bott towers in the context of toric geometry. We show that any kth stage of a Bott tower is a smooth projective toric variety associated to a fan arising from a crosspolytope; conversely, we prove that any toric variety associated to a fan obtained from a crosspolytope actually gives rise to a Bott tower. The former leads us to a description of the tangent bundle of the kth stage of the tower, considered as a complex manifold, which splits into a sum of complex line bundles. Applying Danilov-Jurkiewicz theorem, we compute the cohomology ring of any kth stage, and by way of construction, we provide all the monomial identities defining the related affine toric varieties.