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arXiv · 2607.21457

The restricted Hitchin map of wobbly vector bundles

Clemens Nollau
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Abstract

This article studies the restricted Hitchin map $h_V$ of a stable rank 2 vector bundle $V$ on a smooth projective curve $C$. This map associates to a trace-free twisted endomorphism $φ: V \to V \otimes K_C$ its determinant, which is a quadratic differential. We show that if $V$ is a general wobbly vector bundle, then it has a single nilpotent twisted endomorphism, up to scalars. As a consequence we show that $h_V$ is generically finite and we compute its degree. Furthermore, we show that if $C$ is not hyperelliptic, then the image of $h_V$ contains a quadratic differential with simple zeros. This is equivalent to saying that there is a smooth spectral curve associated to a twisted endomorphism of $V$.

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Clemens Nollau. 2026-07-23. The restricted Hitchin map of wobbly vector bundles. https://arxiv.org/abs/2607.21457

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