arXiv Analytics

Sign in

arXiv:2002.03341 [math.AG]AbstractReferencesReviewsResources

A semi-small decomposition of the Chow ring of a matroid

Tom Braden, June Huh, Jacob P. Matherne, Nicholas Proudfoot, Botong Wang

Published 2020-02-09Version 1

We give a semi-small orthogonal decomposition of the Chow ring of a matroid M. The decomposition is used to give simple proofs of Poincar\'e duality, the hard Lefschetz theorem, and the Hodge-Riemann relations for the Chow ring, recovering the main result of [AHK18]. We also show that a similar semi-small orthogonal decomposition holds for the augmented Chow ring of M.

Comments: 40 pages
Categories: math.AG, math.CO
Related articles: Most relevant | Search more
arXiv:math/0302236 [math.AG] (Published 2003-02-19, updated 2003-09-17)
Hard Lefschetz theorem and Hodge-Riemann relations for intersection cohomology of nonrational polytopes
arXiv:math/0112087 [math.AG] (Published 2001-12-09, updated 2002-12-17)
Hard Lefschetz Theorem for Nonrational Polytopes
arXiv:1911.13253 [math.AG] (Published 2019-11-27)
On the hard Lefschetz theorem for pseudoeffective line bundles

Links

Toolbox