PUBLIC VIVA-VOCE NOTIFICATION
2:00 pm, Lecture Hall 6
On Generalised Parabolic Hitchin Pairs
Sourav Das
Chennai Mathematical Institute.
19-07-19

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Abstract

In this dissertation, we are interested in questions related to the degeneration of moduli of Hitchin pairs. Consider a flat family of curves X over a discrete valuation ring S whose generic fibre is smooth and special fibre is a nodal curve with a single node. Then there exists a flat family of varieties over S whose generic fibre is moduli of stable Hitchin pairs on the generic curve and the special fibre is moduli of stable Gieseker-Hitchin Pairs on the special fibre. In this dissertation, we construct the normalisation of the moduli of stable Gieseker-Hitchin Pairs as the solution to a moduli problem. We also show that there is a birational proper morphism from the normalisation to the moduli space of generalised parabolic Hitchin pairs over the normalisation of the nodal curve.

There is a Hitchin map from the moduli space of generalised parabolic Hitchin pairs to an affine space. We prove that this morphism is proper.