25 citations · 146 across the 36 of their papers we have counts for
11 papers · 1 filter
The moduli space of cubic surfaces and its orbifold fundamental group
Daniel Allcock, Tathagata Basak, Eduard Looijenga
We find a new presentation of the orbifold fundamental group of the moduli space of cubic surfaces, based on the Artin group of the Petersen graph. This group has two well-known qu…
Tropical moduli spaces as symmetric Delta-complexes
Daniel Allcock, Daniel Corey, Sam Payne
We develop techniques for studying fundamental groups and integral singular homology of symmetric Delta-complexes, and apply these techniques to study moduli spaces of stable tropi…
The tetrahedron and automorphisms of Enriques and Coble surfaces of Hessian type
Daniel Allcock, Igor Dolgachev
Consider a cubic surface satisfying the mild condition that it may be described in Sylvester's pentahedral form. There is a well-known Enriques or Coble surface S with K3 cover bir…
Congruence subgroups and Enriques surface automorphisms
Daniel Allcock
We give conceptual proofs of some results on the automorphism group of an Enriques surface X, for which only computational proofs have been available. Namely, there is an obvious u…
A fake plane via 2-adic uniformization with torsion
Daniel Allcock, Fumiharu Kato
We adapt the theory of non-Archimedean uniformization to construct a smooth surface from a lattice in PGL3(Q2) that has nontrivial torsion. It turns out to be a fake projective pla…
Hyperbolic geometry and moduli of real cubic surfaces
Daniel Allcock, James A. Carlson, Domingo Toledo
Let M_0^R be the moduli space of smooth real cubic surfaces. We show that each of its components admits a real hyperbolic structure. More precisely, one can remove some lower-dimen…