Abstract
Representation and character varieties of the Baumslag–Solitar groups 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 Rn(BS(p, q)) are rational varieties of dimension n2, and each irreducible component of the character variety Xn(BS(p, q)) is a rational variety of dimension k ≤ n. The smoothness of irreducible components of the variety Rns (BS(p, q)) of irreducible representations is established, and it is proved that all irreducible components of the variety Rns (BS(p, q)) are isomorphic to A1 {0}.
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