#### Volume 17, issue 2 (2017)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
On the geometry and topology of partial configuration spaces of Riemann surfaces

### Barbu Berceanu, Daniela Anca Măcinic, Ştefan Papadima and Clement Radu Popescu

Algebraic & Geometric Topology 17 (2017) 1163–1188
##### Abstract

We examine complements (inside products of a smooth projective complex curve of arbitrary genus) of unions of diagonals indexed by the edges of an arbitrary simple graph. We use Orlik–Solomon models associated to these quasiprojective manifolds to compute pairs of analytic germs at the origin, both for rank-$1$ and rank-$2$ representation varieties of their fundamental groups, and for degree-$1$ topological Green–Lazarsfeld loci. As a corollary, we describe all regular surjections with connected generic fiber, defined on the above complements onto smooth complex curves of negative Euler characteristic. We show that the nontrivial part at the origin, for both rank-$2$ representation varieties and their degree-$1$ jump loci, comes from curves of general type via the above regular maps. We compute explicit finite presentations for the Malcev Lie algebras of the fundamental groups, and we analyze their formality properties.

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/agt

We have not been able to recognize your IP address 3.239.233.139 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.