The global nilpotent cone on a curve is the locus of nilpotent Higgs fields in the cotangent stack of the moduli stack of principal
bundles. For a smooth projective curve 
and a reductive group with
a suitable invariant form, a cotangent vector
is a bundle 
and a section of 
.
The section is required to be nilpotent at the generic point.
With a Borel reduction 
at a marked point 
, the parabolic version allows a simple
pole and requires
 |
Here 
is the unipotent radical of the chosen Borel subgroup,
and 
is again generically nilpotent.
