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arXiv · 2609.38548

Zero velocity Lagrangians in the Hitchin system

Peter Gothen·André Oliveira·Rodrigo Pereira
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Abstract

Lagrangians of the moduli space of Higgs bundles are a fundamental piece of its study under the lens of mirror symmetry. We construct a new class of Lagrangians defined via a zero 'velocity condition' imposed on the natural action of the non-zero complex numbers on the moduli space, motivated by a certain 'infinitesimal conormal principle'. These are Lagrangian subvarieties analogous to the upward flows considered by [CW19] and [HH22], but which fiber over the $\mathbb{C}^*$-fixed point subvarieties. We then prove a formula for the number of intersection points of this Lagrangian with the generic fiber of the Hitchin map, and build a vector bundle over the dual moduli space which we conjecture to correspond to its mirror hyperholomorphic bundle.

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Peter Gothen, André Oliveira, Rodrigo Pereira. 2026-09-29. Zero velocity Lagrangians in the Hitchin system. https://arxiv.org/abs/2609.38548

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