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  • Stefan Papadima (a1) and Alexander I. Suciu (a2)


We study the germs at the origin of $G$ -representation varieties and the degree 1 cohomology jump loci of fundamental groups of quasi-projective manifolds. Using the Morgan–Dupont model associated to a convenient compactification of such a manifold, we relate these germs to those of their infinitesimal counterparts, defined in terms of flat connections on those models. When the linear algebraic group $G$ is either $\text{SL}_{2}(\mathbb{C})$ or its standard Borel subgroup and the depth of the jump locus is 1, this dictionary works perfectly, allowing us to describe in this way explicit irreducible decompositions for the germs of these embedded jump loci. On the other hand, if either $G=\text{SL}_{n}(\mathbb{C})$ for some $n\geqslant 3$ , or the depth is greater than 1, then certain natural inclusions of germs are strict.



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The first author’s work was partially supported by the Romanian Ministry of Research and Innovation, CNCS–UEFISCDI, grant PN-III-P4-ID-PCE-2016-0030, within PNCDI III. The second author was partially supported by the Simons Foundation collaboration grant for mathematicians 354156.

Deceased 10 January 2018.



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  • Stefan Papadima (a1) and Alexander I. Suciu (a2)


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