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Add to My Calendar

Responsabili:

Federica Galluzzi  ed  Elena Martinengo
 

Nel calendario si indicano i seminari di geometria algebrica e altre attività di interesse, organizzate dall'Università e dal Politecnico di Torino.

Toric variety bundles and their intersection theory

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Data: 

21/01/2025 - 14:30

Aula: 

Aula Lagrange

Speaker: 

Leonid Monin

Categoria: 

Seminari di Algebra e Geometria Algebrica

Afferenza: 

EPFL, Losanna

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.