Bott towers, crosspolytopes and torus actions


Civan Y.

GEOMETRIAE DEDICATA, cilt.113, ss.55-74, 2005 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 113 Konu: 1
  • Basım Tarihi: 2005
  • Doi Numarası: 10.1007/s10711-005-1725-y
  • Dergi Adı: GEOMETRIAE DEDICATA
  • Sayfa Sayıları: ss.55-74

Özet

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.