On representation varieties of some HNN-extensions of free groups
In the article we provide the description of the structure and the properties of representation varieties <i>R</i><sub>n</sub>(<i>G</i>(<i>p</i>,<i>q</i>)) of the groups with the presentation <i>G</i>(<i>p</i>,<i>q</i>) = ‹<i>x</i><sub>1</sub>,…, <i>x</i><sub>2</sub>, <i>t</i>|<i>t</i>(<i>x</i><sub>1</sub><sup>2</sup>…<i>x</i><sub>g</sub><sup>2</sup>)<sup>q</sup>›, where <i>g</i> ≥ 3, |<i>p</i>| > <i>q</i> ≥ 1. Irreducible components of <i>R</i><sub>n</sub>(<i>G</i>(<i>p</i>,<i>q</i>)) are found, their dimensions are calculated and it is proved, that every irreducible component of <i>R</i><sub>n</sub>(<i>G</i>(<i>p</i>,<i>q</i>)) is a rational variety.