Abstract:

We establish that the Hitchin connection is a perturbation of the L₂ connection. We notice that such a formulation of the Hitchin connection does not necessarily require the manifold in question possessing a rigid family of Kähler structures. We then proceed to calculate the asymptotic expansion of general perturbations of the L₂-connection, and see when under certain assumptions such perturbations are at and projectively at. During the calculations we also found an asymptotic expansion of the projection operator $\pi_\sigma^{(k)}$ which projects onto the holomorphic sections of the k-th tensor of prequantum line bundle.

Assesment committee: 
Martin Schlichenmaier (Uni. Luxembourg)
Steen Markvorsen (DTU)
Henning Haahr Andersen (AU), Chair