Date: Thursday, 10 April 2025
Time: 3.30 PM
Venue: Seminar Hall
Tropical Toric Vector Bundles
Bivas Khan
Chennai Mathematical Institute.
10-04-2025

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Abstract

Tropical geometry is a new branch at the interface between algebraic geometry and combinatorics. Tropical geometry is intimately connected with toric geometry. For instance, the tropicalization of a projective toric variety is homeomorphic to the associated lattice polytope. We introduce the notion of tropical toric vector bundles on tropical toric varieties using valuated matroids. Our motivation comes from the work of Di Rocco, Jabbusch, and Smith, where the authors associated realizable matroids to a toric vector bundle. We study splitability on tropical projective lines. In contrast to the classical situation, we show that tropical toric bundles on tropical projective line do not necessarily split. We also study the semistability of such bundles. This is a joint work with Diane Maclagan.