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A proof of the Hodge universality conjecture at nonzero dispersion
Abstract
We prove that a scalar tau-symmetric Hamiltonian deformation of the Riemann hierarchy in generalized standard form is uniquely determined by the nonzero coefficient of ux2 and the coefficients of uxxg, g≥2, in its first Hamiltonian density. This determines the original hierarchy up to normal Miura transformations. Combined with the construction of Hodge-class double ramification hierarchies by Buryak--Rossi, this establishes Hodge universality at nonzero dispersion.
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BibTeX
@misc{iglesias2026proof,
title = {{A proof of the Hodge universality conjecture at nonzero dispersion}},
author = {Francisco Hernández Iglesias},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11469},
eprint = {2609.11469},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11469},
}
RIS
TY - UNPB
TI - A proof of the Hodge universality conjecture at nonzero dispersion
AU - Francisco Hernández Iglesias
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11469
UR - https://arxiv.org/abs/2609.11469
AB - We prove that a scalar tau-symmetric Hamiltonian deformation of the Riemann hierarchy in generalized standard form is uniquely determined by the nonzero coefficient of u_x^2 and the coefficients of u_xx^g, g≥2, in its first Hamiltonian density. This determines the original hierarchy up to normal Miura transformations. Combined with the construction of Hodge-class double ramification hierarchies by Buryak--Rossi, this establishes Hodge universality at nonzero dispersion.
ER -