Séminaire Lotharingien de Combinatoire, 95B.23 (2026), 12 pp.
Raj Gandhi and Ethan Partida
Algebraic Cobordism Rings of Wonderful Varieties and Matroids
Abstract.
We prove a Feichtner-Yuzvinsky presentation and a simplicial
presentation for the algebraic cobordism ring of the toric variety of
the Bergman fan of any loopless matroid in terms of the lattice of
flats of the matroid and the universal formal group law. For an
essential hyperplane arrangement H, we prove that the algebraic
cobordism ring of the wonderful variety WH
of H and the algebraic cobordism ring of the toric variety of
the matroid underlying H are isomorphic, and that both rings
coincide with the complex cobordism ring
of WH.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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