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Combinatorial Algebraic Geometry: Tropical Vector Bundles and their Chern Classes

Andrew Tawfeek (University of Washington)
Friday, March 3, 2023 - 10:30am to 11:20am
Thomson Hall (THO) 325

We introduce the notion of a tropical vector bundle (of rank n) over a tropical cycle X, which is equivalently interpretable as a polyhedral complex living "above" X or GL_n-torsor. Primarily relying on the more-accessible combinatorial definition, we go on to look at morphisms, rational sections, and pull-backs of these bundles. After some examples, we will discuss how one can take local intersection products and construct Chern classes -- concluding the talk with a classification of all vector bundles on a (tropical) elliptic curve up to isomorphism, which will (surprisingly!) coincide with Atiyah's 1957 result in classical algebraic geometry.

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