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

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

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We give a semi-small orthogonal decomposition of the Chow ring of a matroid M. The decomposition is used to give simple proofs of Poincaré duality, the hard Lefschetz theorem, and the Hodge–Riemann relations for the Chow ring, recovering the main result of [1]. We also introduce the augmented Chow ring of M and show that a similar semi-small orthogonal decomposition holds for the augmented Chow ring.

Original languageEnglish (US)
Article number108646
JournalAdvances in Mathematics
Volume409
DOIs
StatePublished - Nov 19 2022

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Chow rings
  • Decomposition theorem
  • Kähler package
  • Matroids
  • Semi-small maps

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