ﻻ يوجد ملخص باللغة العربية
In this paper, we consider a generalization of the theory of Higgs bundles over a smooth complex projective curve in which the twisting of the Higgs field by the canonical bundle of the curve is replaced by a rank 2 vector bundle. We define a Hitchin map and give a spectral correspondence. We also state a Hitchin-Kobayashi correspondence for a generalization of the Hitchin equations to this situation. In a certain sense, this theory lies halfway between the theories of Higgs bundles on a curve and on a higher dimensional variety.
This is a review article on some applications of generalised parabolic structures to the study of torsion free sheaves and $L$-twisted Hitchin pairs on nodal curves. In particular, we survey on the relation between representations of the fundamental
Let $X$ be a compact connected Riemann surface and $D$ an effective divisor on $X$. Let ${mathcal N}_H(r,d)$ denote the moduli space of $D$-twisted stable Higgs bundles (a special class of Hitchin pairs) on $X$ of rank $r$ and degree $d$. It is known
These are the lecture notes from my course in the January 2011 School on Moduli Spaces at the Newton Institute. I give an introduction to Higgs bundles and their application to the study of character varieties for surface group representations.
Over a smooth and proper complex scheme, the differential Galois group of an integrable connection may be obtained as the closure of the transcendental monodromy representation. In this paper, we employ a completely algebraic variation of this idea b
This is a survey article whose main goal is to explain how many components of the character variety of a closed surface are either deformation spaces of representations into the maximal compact subgroup or deformation spaces of certain Fuchsian repre