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

40 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

Access to Document

10.1016/j.aim.2022.108646

Cite this

@article{59f19385c11f4c1a87a5910545eef4c5,

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.",

keywords = "Chow rings, Decomposition theorem, K{\"a}hler package, Matroids, Semi-small maps",

author = "Tom Braden and June Huh and Matherne, \{Jacob P.\} and Nicholas Proudfoot and Botong Wang",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

year = "2022",

month = nov,

day = "19",

doi = "10.1016/j.aim.2022.108646",

language = "English (US)",

volume = "409",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

TY - JOUR

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

UR - https://www.scopus.com/pages/publications/85136002573

UR - https://www.scopus.com/pages/publications/85136002573#tab=citedBy

U2 - 10.1016/j.aim.2022.108646

DO - 10.1016/j.aim.2022.108646

M3 - Article

AN - SCOPUS:85136002573

SN - 0001-8708

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

Access to Document

Other files and links

Fingerprint

Cite this