Parabolic Hitchin Maps and Their Generic Fibers

Abstract

We set up a BNR correspondence for moduli spaces of Higgs bundles over a curve with a parabolic structure over any algebraically closed field. This leads to a concrete description of generic fibers of the associated strongly parabolic Hitchin map. We also show that the global nilpotent cone is equi-dimensional with half dimension of the total space. As a result, we prove the flatness and surjectivity of this map and the existence of very stable parabolic vector bundles.

To appear in Mathematische Zeitschrift. 27 pages, 1 figure,comments welcome

References in corpus (2)

• On the image of the parabolic Hitchin map
• Global nilpotent cone is isotropic : parahoric torsors on curves

Cited by in corpus (3)

• Moduli space of homologically trivial parabolic (Higgs) bundles on the projective line and applications
• Generic Fibers of Parahoric Hitchin Systems
• Monodromy of Rank 2 Parabolic Hitchin Systems