Hitchin pairs on reducible curves

Bhosle, UN (2018) Hitchin pairs on reducible curves. In: International Journal of Mathematics, 29 (3).

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Abstract

We define semistable generalized parabolic Hitchin pairs (GPH) on a disjoint union X of integral smooth curves and construct their moduli spaces. We define a Hitchin map on the moduli space of GPH and show that it is a proper map. We construct moduli spaces of semistable Hitchin pairs on a reducible projective curve Y. When X is the normalization of Y, we give a birational morphism f from the moduli space H of good GPH on X to the moduli spaceM of Hitchin pairs on Y and show that the Hitchin map on H induces a proper Hitchin map on f(H). We determine the fibers of the Hitchin maps. We study the relationship between representations of the (topological) fundamental group of Y and Higgs bundles on Y. We show that if all the irreducible components of Y are smooth, then the Hitchin map is defined on the entire moduli spaceM.

Item Type:	Journal Article
Publication:	International Journal of Mathematics
Publisher:	World Scientific Publishing Co. Pte Ltd
Additional Information:	The copyright for this article belongs to the World Scientific Publishing Co. Pte Ltd.
Keywords:	Curves with many components; Hitchin pairs; stability
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	10 Aug 2022 05:03
Last Modified:	10 Aug 2022 05:03
URI:	https://eprints.iisc.ac.in/id/eprint/75638

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