Global topology of the Hitchin system - GEOM

Hitchin map for SLn and PGLn
for SLn
T ∗
[E] Ň d = H 0 (End0(E) ⊗ K)
that is, a covector at E is given by a trace free Higgs field.
the SLn Hitchin base is
Ǎ = A 0 n
:= H 0 (C, K i ).
the SLn Hitchin map
i=2
ˇχ : T ∗ Ň d → A 0 .
the action of Γ = Pic 0 (C)[n] on T ∗ Ň is along the fibers of ˇχ
⇒ ˇχ descends to the quotient
the PGLn Hitchin map:
ˆχ : (T ∗ Ň )/Γ → Â = A 0 .
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