The Moduli Space of Boundary Compactifications of SL (2, R)

In an earlier paper, the authors introduced the notion of a boundary compactification of SL(2, R) and SL(2, C), a normal projective embedding of PSL2 arising as the Zariski closure of an orbit in (P1)n under the diagonal action of SL2. Here the moduli space of such boundary compactifications of SL(2, R) is shown to be a contractible hyperbolic orbifold, by using the Schwarz–Christoffel transformation to identify it with a quotient of the moduli space of equi-angular planar polygons.