Parabolic Hitchin Maps and Their Generic Fibers
Algebraic Geometry
2021-10-19 v2
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.
Keywords
Cite
@article{arxiv.1906.04475,
title = {Parabolic Hitchin Maps and Their Generic Fibers},
author = {Xiaoyu Su and Bin Wang and Xueqing Wen},
journal= {arXiv preprint arXiv:1906.04475},
year = {2021}
}
Comments
To appear in Mathematische Zeitschrift. 27 pages, 1 figure,comments welcome