The Hitchin fibration is one of the central structures in modern geometry. It connects:
This page collects a recommended path to learn the subject, with references.
The starting point of the whole subject.
Nigel Hitchin (1987) “Stable bundles and integrable systems”
Introduces:
Link: https://doi.org/10.1215/S0012-7094-87-05408-1
PDF: https://people.maths.ox.ac.uk/hitchin/hitchin87.pdf
Key ideas to focus on:
This explains the spectral correspondence.
Beauville – Narasimhan – Ramanan
“Spectral curves and the generalized theta divisor”
Link: https://math.univ-cotedazur.fr/~beauvill/pubs/bnr.pdf
The main result:
(E, φ) ↔ line bundle on spectral curve
Consequences:
Carlos Simpson (1992) “Higgs bundles and local systems”
Link: https://www.numdam.org/item/PMIHES_1992__75__5_0.pdf
Explains the correspondence:
Higgs bundles ↕ flat connections ↕ representations of π₁
Important features:
Gérard Laumon
"Un analogue global du cône nilpotent"
Main result:
Key ideas:
Hausel – Thaddeus
“Mirror symmetry, Langlands duality, and the Hitchin system”
Link: https://arxiv.org/abs/math/0205236
Very good conceptual overview of:
Ngô Bao Châu
Work on the Hitchin fibration used to prove the Fundamental Lemma.
Example reference:
https://arxiv.org/pdf/0801.0446
Key themes:
Tamás Hausel – Hitchin systems
https://hausel.pages.ist.ac.at/wp-content/uploads/sites/229/2024/09/gths.pdf
Good for:
Pavel Etingof and Henry Liu, lecture at BIMSA
Important themes when studying the Hitchin fibration: