Toric vector bundles and tropical geometry

Christopher Manon (U. Kentucky)

09-Sep-2022, 14:00-15:00 (19 months ago)

Abstract: I’ll give an overview of some recent work on the geometry of projectivized toric vector bundles. A toric vector bundle is a vector bundle over a toric variety equipped with an action by the defining torus of the base. As a source of examples, toric vector bundles and their projectivizations provide a rich class of spaces that still manage to admit a combinatorial characterization. I’ll begin with a recent classification result which shows that a toric vector bundle can be captured by an arrangement of points on the Bergman fan of a matroid defined by DiRocco, Jabbusch, and Smith in their work on ”the parliament of polytopes” of a vector bundle. Then I’ll describe how to extract geometric information of the projectivization of the toric vector bundle when this data is nice. I will focus primarily on the Cox ring of the bundle, and the question of whether or not the bundle is a Mori dream space. Then I’ll describe how these properties interact with natural operations on toric vector bundles. This involves the geometry of the closely related class of toric flag bundles and tropical flag varieties. This is joint work with Kiumars Kaveh and Courtney George.

algebraic geometrycombinatorics

Audience: researchers in the topic


(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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Organizers: Alicia Dickenstein*, Ethan Cotterill*, Cristhian Garay López*
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