Singular Hodge theory for combinatorial geometries

By Tom Braden, June Huh, Jacob P. Matherne, Nicholas Proudfoot, Botong Wang. Journal of The American Mathematical Society, 2020

84 citations recorded by the source corpus.

We introduce the intersection cohomology module of a matroid and prove that it satisfies Poincar\'e duality, the hard Lefschetz theorem, and the Hodge-Riemann relations. As applications, we obtain proofs of Dowling and Wilson's Top-Heavy conjecture and the nonnegativity of the coefficients of Kazhdan-Lusztig polynomials for all matroids.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/87e6d61c984f62ebab717c329ef6cbf9978ae5de

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Christopher Eur
2. Hunter Spink
3. Dennis Tseng
4. Andrew Berget

In Discrete Mathematics and Combinatorics

1. Christopher Eur
2. Hunter Spink
3. Dennis Tseng
4. Andrew Berget

In Geometry and Topology

1. Christopher Eur
2. Hunter Spink
3. Dennis Tseng
4. Andrew Berget

Citations in the corpus

• Tautological classes of matroids (2021, background): “An “augmented” variant of the tautological classes of matroids was introduced and studied in [22], leading to a new log-concavity property of matroids and a better understanding of matroid Schubert varieties studied in [11].”