Journal of the American Mathematical Society· 2026Q1
Singular Hodge theory for combinatorial geometries
- 30citations
- Q1SCImago
- 2026year
Short summary
A new intersection cohomology module for matroids is introduced, proving it satisfies Poincaré duality, hard Lefschetz, and Hodge-Riemann relations.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduced intersection cohomology module for matroids.
- Proved module satisfies Poincaré duality, hard Lefschetz, and Hodge-Riemann relations.
- Provided proofs for Dowling and Wilson's Top-Heavy conjecture.
- Established nonnegativity of Kazhdan-Lusztig polynomial coefficients for all matroids.
AI-generated from the title and abstract; the full text is not read.
Abstract
We introduce the intersection cohomology module of a matroid and prove that it satisfies Poincaré 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.
The authors' abstract, as published at the source. Journal of the American Mathematical Society, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics