Descrizione
Abstract:
Toric variety bundles are (partial) equivariant compactifications of the principal torus bundle over arbitrary base. In particular, they form a fibration with a toric variety as a fiber. Toric variety bundles naturally appear in spherical geometry, logarithmic enumerative geometry as well as the study of semiabelian varieties.
In my talk I will present a combinatorial description for toric variety bundles and will give an update about recent work about them. I will mostly focus on the intersection theory of toric variety bundles presenting:
-- Extension of the BKK theorem to the case of toric variety bundles with smooth fiber;
-- Description of Chow cohomology ring via (relative) Minkowski weights with no conditions on the singularity of the fiber;
-- Description of the equivariant cohomology as the ring of piecewise polynomial functions valued in the cohomology of the base.
If time permits, I will also mention a work in progress on classification of Fano toric variety bundles.