The Hitchin fibration is the map from a moduli space of Higgs bundles to the space of characteristic
polynomial coefficients of their Higgs fields. For stable rank-
bundles on a smooth projective complex curve 
of genus 
with fixed determinant of degree coprime to 
and trace-free Higgs field, it is
 |
The coefficient of degree one vanishes because the field is trace-free. Writing 
for the curve
genus and 
,
this proper map has base dimension 
and total-space dimension 
. Its perverse
Leray filtration is compared with character-variety weights in the P=W
conjecture.
Conjecture for 
."
Selecta Math. 28, Article 90, 2022.