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arXiv · 2506.04707

Intersection of two quadrics: modular interpretation and Hitchin morphism

Vladimiro Benedetti·Andreas Höring·Jie Liu
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Abstract

The cotangent bundle $T^*X$ of a smooth intersection $X$ of two quadrics admits a Lagrangian fibration determined by the intrinsic geometry of $X$. We show that this fibration is actually the Hitchin morphism if we endow $X$ with a structure of moduli space of twisted Spin-bundles. This generalises the classical result for threefolds, in which case it recovers the Hitchin fibration for the moduli space of rank two bundles with fixed determinant of odd degree on a curve of genus two.

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Vladimiro Benedetti, Andreas Höring, Jie Liu. 2025-06-05. Intersection of two quadrics: modular interpretation and Hitchin morphism. https://arxiv.org/abs/2506.04707

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