Nonlinear Hodge correspondence for morphisms

Nianzi Li; Mao Sheng

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arXiv · 2607.13450

Nonlinear Hodge correspondence for morphisms

Nianzi Li·Mao Sheng

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Abstract

We study Higgs sections, flat sections, and their higher-dimensional and functorial analogues in the setting of nonlinear harmonic bundles. For a harmonic vector bundle over a compact K\"ahler manifold, a global section is flat if and only if it is a Higgs section. We show that for general nonlinear harmonic bundles this equivalence requires the vanishing of a degree obstruction. We then extend the result to sub-fibrations and to morphisms by interpreting morphisms as graph sub-fibrations in a fiber product.

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Nianzi Li, Mao Sheng. 2026-07-15. Nonlinear Hodge correspondence for morphisms. https://arxiv.org/abs/2607.13450

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