Hitchin pairs on an integral curve

Bhosle, Usha N. ; Parameswaran, A. J. ; Singh, Sanjay Kumar (2014) Hitchin pairs on an integral curve Bulletin des Sciences Mathematiques, 138 (1). pp. 41-62. ISSN 0007-4497

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Related URL: http://dx.doi.org/10.1016/j.bulsci.2013.09.009


Let Y be an integral projective scheme of dimension 1 over a field k (of arbitrary characteristic). We construct the moduli spaces of Hitchin pairs on Y. We define a notion of strong semistability for Hitchin pairs on Y. Assume that the base field is infinite and the normalization of Y is smooth. Then we show that finite direct sums of strongly semistable Hitchin pairs on Y form a neutral Tannakian category. We define the holonomy group scheme GHY of Y to be the Tannakian group scheme for this category. For a strongly semistable G-Hitchin pair, we construct a monodromy group scheme. We study the relation between Higgs bundles on Y and the representations of the (topological) fundamental group of Y in the complex general linear group.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Hitchin Pairs, Curve; Tannakian Category
ID Code:112229
Deposited On:23 Jan 2018 12:10
Last Modified:23 Jan 2018 12:10

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