Tropical geometry of Rado matroids

被引：0

作者：

Buchanan, Calum ^{[1
]}

Danner, Richard ^{[1
]}

机构：

[1] Univ Vermont, Dept Math & Stat, Burlington, VT 05401 USA

来源：

DISCRETE MATHEMATICS LETTERS | 2024年 / 14卷

关键词：

tropical geometry; Chow ring; Rado matroid;

D O I：

10.47443/dml.2024.044

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we characterize the products of simplicial generators for the Chow ring of a loopless matroid, extending a result of Backman, Eur, and Simpson [J. Eur. Math. Soc., DOI: 10.4171/JEMS/1350]. We prove that the stable intersection of a collection of tropical hyperplanes centered at the origin with the Bergman fan of a matroid is the Bergman fan of the dual of a certain Rado matroid.

引用

页码：27 / 30

页数：4

共 13 条

[1] Hodge theory for combinatorial geometries [J].

Adiprasito, Karim ;

Huh, June ;

Katz, Eric .

ANNALS OF MATHEMATICS, 2018, 188 (02) :381-452

[2] Simplicial generation of Chow rings of matroids [J].

Backman, Spencer ;

Eur, Christopher ;

Simpson, Connor .

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2024, 26 (11) :4491-4535

[3]

DECONCINI C, 1995, SELECTA MATH, V1, P459

[4] Intersection Theory of Polymatroids [J].

Eur, Christopher ;

Larson, Matt .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2024, 2024 (05) :4207-4241

[5] Chow rings of toric varieties defined by atomic lattices [J].

Feichtner, EM ;

Yuzvinsky, S .

INVENTIONES MATHEMATICAE, 2004, 155 (03) :515-536

[6] Presentations of transversal valuated matroids [J].

Fink, Alex ;

Olarte, Jorge Alberto .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2022, 105 (01) :24-62

[7] The intersection ring of matroids [J].

Hampe, Simon .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 2017, 122 :578-614

[8]

John Alvah Nash-Williams Crispin St., 1966, Theory of GraphsInternational SymposiumTheorie des graphesJournees internationales detude, P263

[9] K-rings of wonderful varieties and matroids [J].

Larson, Matt ;

Li, Shiyue ;

Payne, Sam ;

Proudfoot, Nicholas .

ADVANCES IN MATHEMATICS, 2024, 441

[10]

Larson M, 2025, Arxiv, DOI arXiv:2402.03444

← 1 2 →