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

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

doi:10.1016/j.aim.2022.108646

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

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

Mathematics

Research output: Contribution to journal › Article › peer-review

24 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 language	English (US)
Article number	108646
Journal	Advances in Mathematics
Volume	409
DOIs	https://doi.org/10.1016/j.aim.2022.108646
State	Published - Nov 19 2022

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Chow rings
Decomposition theorem
Kähler package
Matroids
Semi-small maps

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10.1016/j.aim.2022.108646

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title = "A semi-small decomposition of the Chow ring of a matroid",

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 Poincar{\'e} 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.",

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T1 - A semi-small decomposition of the Chow ring of a matroid

AU - Braden, Tom

AU - Huh, June

AU - Matherne, Jacob P.

AU - Proudfoot, Nicholas

AU - Wang, Botong

PY - 2022/11/19

Y1 - 2022/11/19

N2 - 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.

AB - 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.

KW - Chow rings

KW - Decomposition theorem

KW - Kähler package

KW - Matroids

KW - Semi-small maps

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VL - 409

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 108646

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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