Chern flow and Chern moment algebras
Abstract
We construct realizable-volume models over every field for the factorial normalizations of homogeneous Lascoux, Lascoux-atom, and positive Grothendieck packets, including their minimal homogenizations and layers. In particular, the construction realizes the factorial normalizations of all Schubert and key polynomials and of the minimal sign-corrected homogeneous Grothendieck polynomials. The normalized polynomials are Lorentzian, and the ordinary supports are the lattice points of integral generalized polymatroids. On a Bott--Samelson tower, row and co-row filtrations assemble the local factors into globally generated bundles; a creation-state graph absorbs the remaining kernel factors by Chern flow. We also construct intrinsic algebras of joint Chern moments. Positive inverse-Chern presentations give these algebras Hard Lefschetz and Hodge--Riemann relations, and supply source-level Hodge completions of the packets. For globally generated tropical toric bundles in the sense of Kaveh--Manon, finite generating witnesses and matroid duality provide the presentations required by Larson--Partida's theorem, without representability. These constructions yield joint Chern-number inequalities, nonvanishing polymatroids, and equality criteria.
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BibTeX
@misc{nguyendang2026chern,
title = {{Chern flow and Chern moment algebras}},
author = {Khai-Hoan Nguyen-Dang and Zhenpeng Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02850},
eprint = {2609.02850},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02850},
}
RIS
TY - UNPB
TI - Chern flow and Chern moment algebras
AU - Khai-Hoan Nguyen-Dang
AU - Zhenpeng Wang
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.02850
UR - https://arxiv.org/abs/2609.02850
AB - We construct realizable-volume models over every field for the factorial normalizations of homogeneous Lascoux, Lascoux-atom, and positive Grothendieck packets, including their minimal homogenizations and layers. In particular, the construction realizes the factorial normalizations of all Schubert and key polynomials and of the minimal sign-corrected homogeneous Grothendieck polynomials. The normalized polynomials are Lorentzian, and the ordinary supports are the lattice points of integral generalized polymatroids. On a Bott--Samelson tower, row and co-row filtrations assemble the local factors into globally generated bundles; a creation-state graph absorbs the remaining kernel factors by Chern flow. We also construct intrinsic algebras of joint Chern moments. Positive inverse-Chern presentations give these algebras Hard Lefschetz and Hodge--Riemann relations, and supply source-level Hodge completions of the packets. For globally generated tropical toric bundles in the sense of Kaveh--Manon, finite generating witnesses and matroid duality provide the presentations required by Larson--Partida's theorem, without representability. These constructions yield joint Chern-number inequalities, nonvanishing polymatroids, and equality criteria.
ER -