4 papers · 1 filter
Real Cubic Surfaces and Real Hyperbolic Geometry
Daniel Allcock, James A. Carlson, Domingo Toledo
The moduli space of stable real cubic surfaces is the quotient of real hyperbolic four-space by a discrete, nonarithmetic group. The volume of the moduli space is 37π^2/1080 in the…
The Complex Hyperbolic Geometry of the Moduli Space of Cubic Surfaces
Daniel Allcock, James A. Carlson, Domingo Toledo
Recall that the moduli space of smooth (that is, stable) cubic curves is isomorphic to the quotient of the upper half plane by the group of fractional linear transformations with i…
Cubic Surfaces and Borcherds Products
Daniel Allcock, Eberhard Freitag
The moduli space of cubic surfaces in complex projective space is known to be isomorphic to the quotient of the complex 4-ball by a certain arithmetic group. We apply Borcherds' te…
The Period Lattice for Enriques Surfaces
Daniel Allcock
We simplify the usual statement of the Torelli theorem for complex Enriques surfaces, by means of a lattice-theoretic trick. This allows easy proofs of several known results, which…