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arXiv · 2609.02850

Chern flow and Chern moment algebras

Khai-Hoan Nguyen-Dang·Zhenpeng Wang
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Abstract

We construct realizable-volume models over every field for the factorial normalizations of homogeneous Lascoux, Lascoux-atom, and positive Grothendieck packets. Their layers include key polynomials, Demazure atoms, Schubert polynomials, and sign-corrected Grothendieck components. The normalized polynomials are Lorentzian, and the supports of the ordinary Grothendieck, Lascoux, and Lascoux-atom polynomials are the lattice points of integral generalized polymatroids. The construction assembles local factors on a Bott--Samelson tower into globally generated row and co-row bundles. A creation-state graph of exact sequences absorbs the remaining kernel factors by Chern flow. We also retain the algebra underlying these intersection arrays. Joint Chern moments define an intrinsic Poincar\'e-duality algebra, while a positive inverse-Chern certificate supplies Hard Lefschetz and Hodge--Riemann relations. Geometric evaluation kernels provide such certificates and source-level Hodge completions for the packets and their nonzero layers. A class-valued Hankel pairing describes functoriality and the obstruction to base change. For globally generated tropical toric bundles in the sense of Kaveh--Manon, finite generating witnesses and matroid duality supply the certificates required by Larson--Partida's theorem, yielding joint Chern-number inequalities without a representability assumption. The same moment algebras also yield nonvanishing polymatroids and equality criteria.

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Khai-Hoan Nguyen-Dang, Zhenpeng Wang. 2026-09-02. Chern flow and Chern moment algebras. https://arxiv.org/abs/2609.02850

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