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arXiv · 2609.11469

A proof of the Hodge universality conjecture at nonzero dispersion

Francisco Hernández Iglesias
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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 $u_x^2$ and the coefficients of $u_{xx}^g$, $g\ge2$, 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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Francisco Hernández Iglesias. 2026-09-10. A proof of the Hodge universality conjecture at nonzero dispersion. https://arxiv.org/abs/2609.11469

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