Nonlinear Hodge correspondence for morphisms
arXiv:2607.13450
The paper investigates when a global section of a nonlinear harmonic bundle over a compact Kähler manifold is simultaneously flat and Higgs, showing that this equivalence holds only after a certain degree obstruction vanishes, and extends the analysis to sub‑fibrations and morphisms via graph sub‑fibrations.
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 Kähler 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.
63 pages, comments welcome