can you please recommend me a good reference to learn about the Hitchin fibration in the language of algebraic geometry?
1 Answer
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At the moment I am not sure what to recommend if you want short introduction. But if you something like a longer text giving various perspective is Okay for you I would suggest:
Ron Donagi, Eyal Markman Spectral curves, algebraically completely integrable Hamiltonian systems, and moduli of bundles, http://arxiv.org/abs/alg-geom/9507017.
As a kind of remark, according to my experience looking from solely algebraic geometry point of view is somehow not quite good to get complete understanding. I am not aware of any "natural" explanation why Hitchin's hamiltonians Poisson commute (i.e. fibration would be Lagragian) given in terms of algebraic geometry. Original Hitchin's approach is via differential geometry and Beilinson-Drinfeld point of view is via representation theory.
answered Jan 26, 2014 at 9:55