Geodesic
Representation and character varieties of the Baumslag--Solitar groups
Informatics and Automation, Algebra, geometry, and number theory, Tome 292 (2016), pp. 26-42.

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Representation and character varieties of the Baumslag–Solitar groups $\mathrm {BS}(p,q)$ are analyzed. Irreducible components of these varieties are found, and their dimension is calculated. It is proved that all irreducible components of the representation variety $R_n(\mathrm {BS}(p,q))$ are rational varieties of dimension $n^2$, and each irreducible component of the character variety $X_n(\mathrm {BS}(p,q))$ is a rational variety of dimension $k\le n$. The smoothness of irreducible components of the variety $R_n^\mathrm s(\mathrm {BS}(p,q))$ of irreducible representations is established, and it is proved that all irreducible components of the variety $X_n^\mathrm s(\mathrm {BS}(p,q))$ are isomorphic to $\mathbb {A}^1\setminus \{0\}$. 
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V. V. Benyash-Krivets; I. O. Govorushko. Representation and character varieties of the Baumslag--Solitar groups. Informatics and Automation, Algebra, geometry, and number theory, Tome 292 (2016), pp. 26-42. http://geodesic.mathdoc.fr/item/TRSPY_2016_292_a2/

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