Realizability of general normalized Schubert polynomials

Establish whether general normalized Schubert polynomials admit realizable-volume polynomial models over the relevant fields, extending the paper’s realizability result for ordinary single-alphabet type-A Schubert polynomials.

Background

The paper constructs realizable-volume models for ordinary single-alphabet type-A Schubert polynomials and several related polynomial packets, thereby proving corresponding Lorentzian and support conjectures. Its scope is explicitly limited to ordinary single-alphabet statements and does not settle broader realizability questions. The cited survey identifies realizability for general normalized Schubert polynomials as an open problem, leaving open the extension from the ordinary setting treated here to the general class.

References

Huh's 2026 survey records the realizability of general normalized Schubert polynomials as open.

— Canonical-row Chern flow on Bott--Samelson towers: realizable-volume models for Schubert, Grothendieck, and Lascoux polynomials  (2609.02850 - Nguyen-Dang et al., 2 Sep 2026) in Section 1, subsection “Geometric context and proof strategy”