Remarks on the intersection of two quadrics

2025/06/30 by Hitchin, Nigel · 1 citation
#14H60 #14H70 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.23671

Abstract

The article takes the formula for the integrable system defined by Beauville et al on the cotangent bundle of the intersection of two quadrics X, and interprets it in terms of rank 2 quasi parabolic Higgs bundles on the projective line. We then discuss aspects related to the geometric Langlands programme in this simple concrete context. We conclude with a description of the link with the recent paper of Benedetti et al identifying X and its integrable system in terms of invariant Spin(2g) bundles on a hyperelliptic curve of genus g.

Citations

• Intersection of two quadrics: modular interpretation and Hitchin morphism
• Hitchin systems and their quantization
• Twistor Hecke eigensheaves in genus 2
• A general framework for the analytic Langlands correspondence
• Symmetric tensors on the intersection of two quadrics and Lagrangian fibration
• Multiplicity algebras for rank 2 bundles on curves of small genus
• Enhanced mirror symmetry for Langlands dual Hitchin systems

Cited by

• A universal Higgs bundle moduli space

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