ﻻ يوجد ملخص باللغة العربية
When the cohomology ring of a generalized Bott manifold with $mathbb{Q}$-coefficient is isomorphic to that of a product of complex projective spaces $mathbb{C}P^{n_i}$, the generalized Bott manifold is said to be $mathbb{Q}$-trivial. We find a necessary and sufficient condition for a generalized Bott manifold to be $mathbb{Q}$-trivial. In particular, every $mathbb{Q}$-trivial generalized Bott manifold is diffeomorphic to a $prod_{n_i>1}mathbb{C}P^{n_i}$-bundle over a $mathbb{Q}$-trivial Bott manifold.
To a direct sum of holomorphic line bundles, we can associate two fibrations, whose fibers are, respectively, the corresponding full flag manifold and the corresponding projective space. Iterating these procedures gives, respectively, a flag Bott tow
In the present paper, we characterize Fano Bott manifolds up to diffeomorphism in terms of three operations on matrix. More precisely, we prove that given two Fano Bott manifolds $X$ and $X$, the following conditions are equivalent: (1) the upper tri
In this article the generic torus orbit closure in a flag Bott manifold is shown to be a non-singular toric variety, and its fan structure is explicitly calculated.
By Delzants theorem, closed symplectic toric manifolds are classified by the images of moment maps. In the case of a generalized Bott manifold, this image is a polytope $P$ combinatorially equivalent to the product of simplices. We compute the Gromov
In this article we introduce flag Bott manifolds of general Lie type as the total spaces of iterated flag bundles. They generalize the notion of flag Bott manifolds and generalized Bott manifolds, and admit nice torus actions. We calculate the torus