Geodesic
On representation varieties of some HNN-extensions of free groups
Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2018), pp. 10-16

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In the article we provide the description of the structure and the properties of representation varieties $R_{n}(G(p,q))$ of the groups with the presentation $G(p,q)=\langle x_{1},\dots , x_{2},t|t(x_{1}^{2}\dots x_{g}^{2})=(x_{1}^{2}\dots x_{g}^{2})^{q}\rangle$, where $g\geq 3, |p|>q\geq 1$. Irreducible components of $R_{n}(G(p,q))$ are found, their dimensions are calculated and it is proved, that every irreducible component of $R_{n}(G(p,q))$ is a rational variety.
Keywords: a group presentation, a representation variety, a dimension of a variety, a rational variety. 
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     author = {A. N. Admiralova and V. V. Benyash-Krivets},
     title = {On representation varieties of some {HNN-extensions} of free groups},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {10--16},
     publisher = {mathdoc},
     volume = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2018_2_a1/}
}
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A. N. Admiralova; V. V. Benyash-Krivets. On representation varieties of some HNN-extensions of free groups. Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2018), pp. 10-16. http://geodesic.mathdoc.fr/item/BGUMI_2018_2_a1/