ITERATED WEIGHTED PROJECTIVE SPACE FIBRATIONS AND TORIC ORBIFOLDS
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We generalize classical generalized Bott towers to orbifolds using weighted projectivizations of line bundles, which we call weighted projective towers. From the perspective of toric topology, such a space can be constructed from a product of simplices with a rational characteristic function on it. However, such a construction gives an orbifold fibration in general. Our main theorem provides explicit criteria for when a toric orbifold over a product of simplices admits a structure of a weighted projective tower.
Abstract
We generalize classical generalized Bott towers to orbifolds using weighted projectivizations of line bundles, which we call weighted projective towers. From the perspective of toric topology, such a space can be constructed from a product of simplices with a rational characteristic function on it. However, such a construction gives an orbifold fibration in general. Our main theorem provides explicit criteria for when a toric orbifold over a product of simplices admits a structure of a weighted projective tower.