61 citations · 148 across the 12 of their papers we have counts for
16 papers
One-cusped complex hyperbolic 2-manifolds
Martin Deraux, Matthew Stover
This paper builds one-cusped complex hyperbolic -manifolds by an explicit geometric construction. Specifically, for each odd there is a smooth projective surface …
Mirror stabilizers for lattice complex hyperbolic triangle groups
Martin Deraux
For each lattice complex hyperbolic triangle group, we study the Fuchsian stabilizer of a reprentative of each group orbit of mirrors of complex reflections. We give explicit gener…
Torsion in 1-cusped Picard modular groups
Martin Deraux, Mengmeng Xu
We present a systematic effective method to construct coarse fundamental domains for the action of the Picard modular groups where has class…
On the geometry of a Picard modular group
Martin Deraux
We study geometric properties of the action of the Picard modular group on the complex hyperbolic plane , where denotes th…
Volumes of 3-ball quotients as intersection numbers
Martin Deraux
We give an explicit description of the 3-ball quotients constructed by Couwenberg-Heckman-Looijenga, and deduce the value of their orbifold Euler characteristics. For each lattice,…
A new non-arithmetic lattice in PU(3,1)
Martin Deraux
We study the arithmeticity of the Couwenberg-Heckman-Looijenga lattices in PU(n,1), and show that they contain a non-arithmetic lattice in PU(3,1) which is not commensurable to the…
Non-arithmetic ball quotients from a configuration of elliptic curves in an Abelian surface
Martin Deraux
We construct some non-arithmetic ball quotients as branched covers of a quotient of an Abelian surface by a finite group, and compare them with lattices that previously appear in t…
New non-arithmetic complex hyperbolic lattices II
Martin Deraux, John R. Parker, Julien Paupert
We describe a general procedure to produce fundamental domains for complex hyperbolic triangle groups, a class of groups that contains a representative of the commensurability clas…
Non-arithmetic lattices and the Klein quartic
Martin Deraux
We give an algebro-geometric construction of some of the non-arithmetic ball quotients constructed by the author, Parker and Paupert. The new construction reveals a relationship be…
A 1-parameter family of spherical CR uniformizations of the figure eight knot complement
Martin Deraux
We describe a simple fundamental domain for the holonomy group of the boundary unipotent spherical CR uniformization of the figure eight knot complement, and deduce that small defo…
On spherical CR uniformization of 3-manifolds
Martin Deraux
We consider the discrete representations of 3-manifold groups into that appear in the Falbel-Koseleff-Rouillier census, such that the peripheral subgroups have cyclic uni…
New non-arithmetic complex hyperbolic lattices
Martin Deraux, John R. Parker, Julien Paupert
We produce a family of new, non arithmetic lattices in PU(2,1). All previously known examples were commensurable with lattices constructed by Picard, Mostow and Deligne-Mostow, and…
Complex hyperbolic geometry of the figure eight knot
Martin Deraux, Elisha Falbel
We show that the figure eight knot complement admits a uniformizable spherical CR structure, i.e. it occurs as the manifold at infinity of a complex hyperbolic orbifold. The unifor…
Census of the complex hyperbolic sporadic triangle groups
Martin Deraux, John R. Parker, Julien Paupert
The goal of this paper is to give a conjectural census of complex hyperbolic sporadic groups. We prove that only finitely many of these sporadic groups are lattices. We also give a…
Almost quarter-pinched Kähler metrics and Chern numbers
Martin Deraux, Harish Seshadri
We prove that compact Kähler manifolds whose sectional curvatures are close to 1/4-pinched have ratios of Chern numbers close to the corresponding ratios of a complex hyperbolic sp…
Forgetful maps between Deligne-Mostow ball quotients
Martin Deraux
We study forgetful maps between Deligne-Mostow moduli spaces of weighted points on P^1, and classify the forgetful maps that extend to a map of orbifolds between the stable complet…