Global topology of the Hitchin system - GEOM
Global topology of the Hitchin system - GEOM
Global topology of the Hitchin system - GEOM
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Symmetries <strong>of</strong> <strong>the</strong> GLn and PGLn <strong>Hitchin</strong> fibration<br />
for GLn: fix a ∈ Areg<br />
tensor product gives a simply transitive action <strong>of</strong> Pic 0 (Ca) on<br />
Jac d (Ca)<br />
❀ Ma is a torsor for Pa := Pic 0 (Ca)<br />
for PGLn: fix a ∈ A 0 reg<br />
ˆMa = Ma/ Pic 0 (C)<br />
is a torsor for <strong>the</strong> quotient ˆPa := Pa/ Pic 0 (C) abelian variety<br />
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