Abstract:

It is well known that under certain conditions, for an elliptic surface X --> C over the field of complex numbers, we have a natural isomorphism of fundamental group of X and the orbifold fundamental group of C (orbifold structure is determined by the multiple fibers). Hence the space of finite dimensional complex representations of the above groups are naturally in bijective correspondence. On thee otherhand we have from the work of Donaldson,simpson,corelette, Hitchin et al, that these spaces can be identified with certain spaces of higgs bundles on X and C. In this talk our aim is to establish an algebraic geometric correspondence between these spaces.

This work is motivated by a paper of Stefan Baur where such a correspondence was demonstrated in the case of unitary representations (higgs field is zero).

It is well known that under certain conditions, for an elliptic surface X --> C over the field of complex numbers, we have a natural isomorphism of fundamental group of X and the orbifold fundamental group of C (orbifold structure is determined by the multiple fibers). Hence the space of finite dimensional complex representations of the above groups are naturally in bijective correspondence. On thee otherhand we have from the work of Donaldson,simpson,corelette, Hitchin et al, that these spaces can be identified with certain spaces of higgs bundles on X and C. In this talk our aim is to establish an algebraic geometric correspondence between these spaces.

This work is motivated by a paper of Stefan Baur where such a correspondence was demonstrated in the case of unitary representations (higgs field is zero).