arXiv subjects

Philip A. Foth

Publications and source records attributed to Philip A. Foth.

2 recordsLinked to original sources

arXiv1997

Deformations of representations of fundamental groups of open Kaehler manifolds

Given a compact Kaehler manifold, we consider the complement U of a divisor with normal crossings. We study the variety of unitary representations of the fundamental group of U with certain restrictions related to the divisor. We show that the possible singularities of this variety as well as of the corresponding moduli space of irreducible representations are quadratic. In the course of our proof we exhibit a differential graded Lie algebra of which reflects our deformation problem.

dg-ga↗

arXiv1997

Geometry of Moduli Spaces of Flat Bundles on Punctured Surfaces

We consider the moduli spaces of flat $SL(n, C)$-bundles on Riemann surfaces with one puncture when we fix the conjugacy class ${\cal C}$ of the monodromy transformation around the puncture. We show that under a certain condition on the class ${\cal C}$ (namely the product of $k 1$ and $A_1A_2\cdots A_pA_1^{-1}A_2^{-1}\cdots A_p^{-1}$ belongs to a class which satisfies property P then the $p$ -tuple $(A_1, ..., A_p)$ algebraically generates the whole group $G$.

alg-geom↗