Bott towers, crosspolytopes and torus actions
GEOMETRIAE DEDICATA, cilt.113, sa.1, ss.55-74, 2005 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 113 Sayı: 1
- Basım Tarihi: 2005
- Doi Numarası: 10.1007/s10711-005-1725-y
- Dergi Adı: GEOMETRIAE DEDICATA
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.55-74
- Süleyman Demirel Üniversitesi Adresli: Evet
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.