Summary: Hyperbolic Geometry and the Moduli Space of
Real Binary Sextics
Daniel Allcock, James A. Carlson and Domingo Toledo
Abstract. The moduli space of real 6-tuples in CP 1
is modeled on a quotient
of hyperbolic 3-space by a nonarithmetic lattice in Isom H3
. This is partly
an expository note; the first part of it is an introduction to orbifolds and
hyperbolic reflection groups.
These notes are an exposition of the key ideas behind our result that the
moduli space Ms of stable real binary sextics is the quotient of real hyperbolic
by a certain Coxeter group (together with its diagram automorphism).
We hope they can serve as an aid in understanding our work  on moduli of real
cubic surfaces, since exactly the same ideas are used, but the computations are
easier and the results can be visualized.
These notes derive from the first author's lectures at the summer school
"Algebra and Geometry around Hypergeometric Functions", held at Galatasary
University in Istanbul in July 2005. He is grateful to the organizers, fellow speakers
and students for making the workshop very rewarding. To keep the flavor of lec-