Hodge theory for combinatorial projective bundles
Algebraic Geometry
2026-04-24 v1 Combinatorics
Abstract
We prove the Hard Lefschetz theorem and Hodge-Riemann relations for certain rings which resemble the cohomology rings of projectivizations of globally generated vector bundles over toric varieties. This proves new cases of the standard conjecture of Hodge type and gives Bloch-Gieseker-type results for tautological classes of matroids.
Cite
@article{arxiv.2604.21925,
title = {Hodge theory for combinatorial projective bundles},
author = {Matt Larson and Ethan Partida},
journal= {arXiv preprint arXiv:2604.21925},
year = {2026}
}