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Publications (49)

math.AG2015

Multiple realizations of varieties as ball quotient compactifications

Luca F. Di Cerbo, Matthew Stover

We study the number of distinct ways in which a smooth projective surface $X$ can be realized as a smooth toroidal compactification of a ball quotient. It follows from work of Hirz…

math.GT2025

One-cusped complex hyperbolic 2-manifolds

Martin Deraux, Matthew Stover

This paper builds one-cusped complex hyperbolic $2$ -manifolds by an explicit geometric construction. Specifically, for each odd $d \geq 1$ there is a smooth projective surface $Z_{d}$ …

math.GT2013

On the number of ends of rank one locally symmetric spaces

Matthew Stover

Let Y be a noncompact rank one locally symmetric space of finite volume. Then Y has a finite number e(Y) > 0 of topological ends. In this paper, we show that for any natural number…

math.GT2011

Arithmeticity of complex hyperbolic triangle groups

Matthew Stover

Complex hyperbolic triangle groups were first considered by Mostow in building the first nonarithmetic lattices in PU(2, 1). They are a natural generalization of the classical tria…

math.GR2025

Residual finiteness and discrete subgroups of Lie groups

Matthew Stover

Let $G$ be a real Lie group and $I^ < G$ be a discrete subgroup of $G$ . Is $I^$ residually finite? This paper describes known positive and negative results then poses some questions…

math.CO2017

Explicit bounds from the Alon-Boppana theorem

Joseph Richey, Noah Shutty, Matthew Stover

The purpose of this paper is to give explicit methods for bounding the number of vertices of finite $k$ -regular graphs with given second eigenvalue. Let $X$ be a finite $k$ -regular…

math.GT2011

Cusps of Picard modular surfaces

Matthew Stover

We determine the number of cusps of minimal Picard modular surfaces. The proof also counts cusps of other Picard modular surfaces of arithmetic interest. Consequently, for each N >…

math.GT2020

Arithmeticity, Superrigidity, and Totally Geodesic Submanifolds

Uri Bader, David Fisher, Nick Miller +1

Let $I^$ be a lattice in $SO_{0} (n, 1)$ . We prove that if the associated locally symmetric space contains infinitely many maximal totally geodesic subspaces of dimension at…

math.AG2019

Commensurability Classes of Fake Quadrics

Benjamin Linowitz, Matthew Stover, John Voight

A fake quadric is a smooth projective surface that has the same rational cohomology as a smooth quadric surface but is not biholomorphic to one. We provide an explicit classificati…

math.GT2015

Geodesic curves on Shimura surfaces

Ted Chinburg, Matthew Stover

We parametrize the commensurability classes of curves on Shimura surfaces that are totally geodesic, i.e., the commensurability classes of so-called $C$ -Fuchsian subgroups…

math.GT2019

Congruence RFRS towers

Ian Agol, Matthew Stover

We describe a criterion for a real or complex hyperbolic lattice to admit a RFRS tower that consists entirely of congruence subgroups. We use this to show that certain Bianchi grou…

math.AG2018

On general type surfaces with $q = 1$ and $c_{2} = 3 p_{g}$

Matthew Stover

Let $S$ be a minimal surface of general type with irregularity $q (S) = 1$ . Well-known inequalities between characteristic numbers imply that $3 p_{g} (S) \leq c_{2} (S) \leq 10 p_{g} (S)$ , wh…

math.NT2014

Presentations for quaternionic $S$ -unit groups

Ted Chinburg, Holley Friedlander, Sean Howe +5

The purpose of this paper is to give presentations for projective $S$ -unit groups of the Hurwitz order in Hamilton's quaternions over the rational field $Q$ . To our knowle…

math.GT2016

Bielliptic ball quotient compactifications and lattices in PU(2, 1) with finitely generated commutator subgroup

Luca F. Di Cerbo, Matthew Stover

We construct two infinite families of ball quotient compactifications birational to bielliptic surfaces. For each family, the volume spectrum of the associated noncompact finite vo…

math.GT2016

Parametrizing Shimura subvarieties of $A_{1}$ Shimura varieties and related geometric problems

Benjamin Linowitz, Matthew Stover

This paper gives a complete parametrization of the commensurability classes of totally geodesic subspaces of irreducible arithmetic quotients of $X_{a, b} = (\mathbf{H}^2)^a \times…

math.GT2025

High dimensional hyperbolic Coxeter groups that virtually fiber

Jean-Francois Lafont, Barry Minemyer, Gangotryi Sorcar +2

This paper provides an iterative procedure for constructing hyperbolic Coxeter groups that virtually fiber over $Z$ that is flexible enough to yield infinitely many isomor…

math.GT2020

Azumaya algebras and canonical components

Ted Chinburg, Alan W. Reid, Matthew Stover

Let $M$ be a compact 3-manifold and $I^ = I ¨ _{1} (M)$ . Work of Thurston and Culler--Shalen established the $SL_{2} (C)$ character variety $X (I^)$ as fundamental tool in t…

math.GR2019

New nonlinear hyperbolic groups

Richard Canary, Matthew Stover, Konstantinos Tsouvalas

We construct nonlinear hyperbolic groups which are large, torsion-free, one-ended, and admit a finite $K (I ¨ , 1)$ . Our examples are built from superrigid cocompact rank one lattices…

math.AG2024

Algebraic fundamental groups of fake projective planes

Matthew Stover

Fundamental groups of fake projective planes fall into fifty distinct isomorphism classes, one for each complex conjugate pair. We prove that this is not the case for their algebra…

math.GT2018

Cusp and $b_{1}$ growth for ball quotients and maps onto $Z$ with finitely generated kernel

Matthew Stover

Let $M = B^{2} / I^$ be a smooth ball quotient of finite volume with first betti number $b_{1} (M)$ and let $E (M) \geq 0$ be the number of cusps (i.e., topological end…

math.GT2025

Profinite rigidity of KÃ¤hler groups: Riemann surfaces and subdirect products

Sam Hughes, Claudio Llosa Isenrich, Pierre Py +2

This paper establishes strong profinite rigidity results for KÃ¤hler groups, showing that certain groups are determined within the class of residually finite KÃ¤hler groups by thei…

math.GT2018

Punctured spheres in complex hyperbolic surfaces and bielliptic ball quotient compactifications

Luca F. Di Cerbo, Matthew Stover

In this paper, we study punctured spheres in two dimensional ball quotient compactifications $(X, D)$ . For example, we show that smooth toroidal compactifications of ball quotients…

math.GT2026

Cocompact Fuchsian groups with a modular embedding

Matthew Stover

A Fuchsian group $I^$ has a modular embedding if its adjoint trace field is a totally real number field and every unbounded Galois conjugate $I^^{I ¨} $ comes equipped with a holomorph…

math.AG2020

Geometry of the Wiman-Edge monodromy

Matthew Stover

The Wiman-Edge pencil is a pencil of genus $6$ curves for which the generic member has automorphism group the alternating group $A_{5}$ . There is a unique smooth member, t…

math.GR2016

Character varieties and actions on products of trees

David Fisher, Michael Larsen, Ralf Spatzier +1

It is well known that surface groups admit free and proper actions on finite products of infinite valence trees. In this note, we address the question of whether there can be a fre…

math.AG2026

Automorphisms of the moduli space of smooth cubic surfaces and its fundamental group

Gregorio Baldi, Benson Farb, Ariyan Javanpeykar +1

Let $C$ be the moduli space of smooth complex cubic surfaces and let $I ¨ _{1} (C)$ be its (orbifold) fundamental group. We prove that the ``divisor subgroup'' of $Ï…

math.GT2007

Property (FA) and lattices in SU(2,1)

Matthew Stover

In this paper we consider Property (FA) for lattices in SU(2,1). First, we prove that SU(2,1;O_3) has Property (FA). We then prove that the arithmetic lattices in SU(2,1) of second…

math.GT2024

Products of curves as ball quotients

Matthew Stover

For any $g_{1}, g_{2} \geq 0$ , this paper shows that there is a cocompact lattice $I^ < PU (2, 1)$ such that the ball quotient $I^\ B^{2}$ is birational to a produ…

math.GT2012

Covolumes of nonuniform lattices in PU(n, 1)

Vincent Emery, Matthew Stover

This paper studies the covolumes of nonuniform arithmetic lattices in PU(n, 1). We determine the smallest covolume nonuniform arithmetic lattices for each n, the number of minimal…

math.GT2025

Finite groups and complex projective surfaces

Alexander Lubotzky, Matthew Stover

In response to a question raised by Belolipetsky and the first author, we prove that for every finite group $G$ there are infinitely many isomorphism classes of compact complex hyp…

math.AG2021

Residually finite lattices in $PU (2, 1)$ and fundamental groups of smooth projective surfaces

Matthew Stover, Domingo Toledo

This paper studies residual finiteness of lattices in the universal cover of $PU (2, 1)$ and applications to the existence of smooth projective varieties with fundamental gr…

math.GT2011

Volumes of Picard modular surfaces

Matthew Stover

We show that the conjectural cusped complex hyperbolic 2-orbifolds of minimal volume are the two smallest arithmetic complex hyperbolic 2-orbifolds. We then show that every arithme…

math.AG2019

Rigid surfaces arbitrarily close to the Bogomolov--Miyaoka--Yau line

Matthew Stover, Giancarlo UrzÃºa

We prove the existence of rigid compact complex surfaces of general type whose Chern slopes are arbitrarily close to the Bogomolov--Miyaoka--Yau bound of $3$ . In addition, each of…

math.GT2016

Constructing Geometrically Equivalent Hyperbolic Orbifolds

D. B. McReynolds, Jeffrey S. Meyer, Matthew Stover

In this paper, we construct families of nonisometric hyperbolic orbifolds that contain the same isometry classes of nonflat totally geodesic subspaces. The main tool is a variant o…

math.GT2012

Collisions at infinity in hyperbolic manifolds

D. B. McReynolds, Alan W. Reid, Matthew Stover

For a complete, finite volume real hyperbolic n-manifold M, we investigate the map between homology of the cusps of M and the homology of $M$ . Our main result provides a proof of a…

math.AG2024

Rich representations and superrigidity

Gregorio Baldi, Nicholas Miller, Matthew Stover +1

We investigate and compare applications of the Zilber-Pink conjecture and dynamical methods to rigidity problems for arithmetic real and complex hyperbolic lattices. Along the way…

math.GT2026

A hyperbolic $4$ -orbifold with underlying space $P^{2}$

Matthew Stover

This paper shows that the complex projective plane $P^{2}$ can be realized as the underlying space for a closed hyperbolic $4$ -orbifold. This is the first example of a close…

math.GT2019

Negative curves of small genus on surfaces

Ted Chinburg, Matthew Stover

Let $X$ be an irreducible smooth geometrically integral projective surface over a field. In this paper we give an effective bound in terms of the Neron--Severi rank $I ¨ (X)$ of $X$ …

math.GT2017

Amalgam Anosov representations

Richard D. Canary, Michelle Lee, Matthew Stover

Let $I^$ be a one-ended, torsion-free hyperbolic group and let $G$ be a semisimple Lie group with finite center. Using the canonical JSJ splitting due to Sela, we define amalgam An…

math.GT2018

Finiteness of Maximal Geodesic Submanifolds in Hyperbolic Hybrids

David Fisher, Jean-FranÃ§ois Lafont, Nicholas Miller +1

We show that large classes of non-arithmetic hyperbolic $n$ -manifolds, including the hybrids introduced by Gromov and Piatetski-Shapiro and many of their generalizations, have only…

math.GT2012

A Cantor set with hyperbolic complement

Juan Souto, Matthew Stover

We construct a Cantor set in S^3 whose complement admits a complete hyperbolic metric.

math.NT2014

Small generators for S-unit groups of division algebras

Ted Chinburg, Matthew Stover

Let $k$ be a number field, suppose that $B$ is a central simple division algebra over $k$ , and choose any maximal order $D$ of $B$ . The object of this paper is to show th…

math.AG2017

Classification and arithmeticity of toroidal compactifications with $3 c ˉ_{2} = c ˉ_{1}^{2} = 3$

Luca F. Di Cerbo, Matthew Stover

We classify the minimum volume smooth complex hyperbolic surfaces that admit smooth toroidal compactifications, and we explicitly construct their compactifications. There are five…

math.DS2023

Arithmeticity, superrigidity and totally geodesic submanifolds of complex hyperbolic manifolds

Uri Bader, David Fisher, Nicholas Miller +1

For $n \geq 2$ , we prove that a finite volume complex hyperbolic $n$ -manifold containing infinitely many maximal properly immersed totally geodesic submanifolds of dimension at leas…

math.GT2018

Lattices in $PU (n, 1)$ that are not profinitely rigid

Matthew Stover

Using conjugation of Shimura varieties, we produce nonisomorphic, cocompact, torsion-free lattices in $PU (n, 1)$ with isomorphic profinite completions for all $n \geq 2$ . Th…

math.AG2025

Cohomological nonvanishing for algebraic fundamental groups of ball quotients

Matthew Stover

Suppose $I^ < PU (n, 1)$ is a cocompact arithmetic lattice of simplest type with profinite completion $I^$ . This paper proves there is an open subgroup $\widehatÎ_0…

math.GT2025

Complex hyperbolic 2-orbifolds with isolated singularities

Alan W. Reid, Matthew Stover

For each prime $p$ , this paper constructs compact complex hyperbolic $2$ -manifolds with an isometric action of $Z / p Z$ that is not free and has only isolated fi…

math.AG2021

Residual finiteness for central extensions of lattices in $PU (n, 1)$ and negatively curved projective varieties

Matthew Stover, Domingo Toledo

We study residual finiteness for cyclic central extensions of cocompact arithmetic lattices $I^ < PU (n, 1)$ simple type. We prove that the preimage of $I^$ in any connected…

math.GT2014

Hurwitz ball quotients

Matthew Stover

We consider the analogue of Hurwitz curves, smooth projective curves $C$ of genus $g \geq 2$ that realize equality in the Hurwitz bound $∣ Aut (C) ∣ \leq 84 (g - 1)$ , to smooth…

Publications (49)

Multiple realizations of varieties as ball quotient compactifications

One-cusped complex hyperbolic 2-manifolds

On the number of ends of rank one locally symmetric spaces

Arithmeticity of complex hyperbolic triangle groups

Residual finiteness and discrete subgroups of Lie groups

Explicit bounds from the Alon-Boppana theorem

Cusps of Picard modular surfaces

Arithmeticity, Superrigidity, and Totally Geodesic Submanifolds

Commensurability Classes of Fake Quadrics

Geodesic curves on Shimura surfaces

Congruence RFRS towers

On general type surfaces with q=1 and c2​=3pg​

Presentations for quaternionic S-unit groups

Bielliptic ball quotient compactifications and lattices in PU(2, 1) with finitely generated commutator subgroup

Parametrizing Shimura subvarieties of A1​ Shimura varieties and related geometric problems

High dimensional hyperbolic Coxeter groups that virtually fiber

Azumaya algebras and canonical components

New nonlinear hyperbolic groups

Algebraic fundamental groups of fake projective planes

Cusp and b1​ growth for ball quotients and maps onto Z with finitely generated kernel

Profinite rigidity of KÃ¤hler groups: Riemann surfaces and subdirect products

Punctured spheres in complex hyperbolic surfaces and bielliptic ball quotient compactifications

Cocompact Fuchsian groups with a modular embedding

Geometry of the Wiman-Edge monodromy

Character varieties and actions on products of trees

Automorphisms of the moduli space of smooth cubic surfaces and its fundamental group

Property (FA) and lattices in SU(2,1)

Products of curves as ball quotients

Covolumes of nonuniform lattices in PU(n, 1)

Finite groups and complex projective surfaces

Residually finite lattices in PU(2,1)​ and fundamental groups of smooth projective surfaces

Volumes of Picard modular surfaces

Rigid surfaces arbitrarily close to the Bogomolov--Miyaoka--Yau line

Constructing Geometrically Equivalent Hyperbolic Orbifolds

Collisions at infinity in hyperbolic manifolds

Rich representations and superrigidity

A hyperbolic 4-orbifold with underlying space P2

Negative curves of small genus on surfaces

Amalgam Anosov representations

Finiteness of Maximal Geodesic Submanifolds in Hyperbolic Hybrids

A Cantor set with hyperbolic complement

Small generators for S-unit groups of division algebras

Classification and arithmeticity of toroidal compactifications with 3cˉ2​=cˉ12​=3

Arithmeticity, superrigidity and totally geodesic submanifolds of complex hyperbolic manifolds

Lattices in PU(n,1) that are not profinitely rigid

Cohomological nonvanishing for algebraic fundamental groups of ball quotients

Complex hyperbolic 2-orbifolds with isolated singularities

Residual finiteness for central extensions of lattices in PU(n,1) and negatively curved projective varieties

Hurwitz ball quotients

On general type surfaces with $q = 1$ and $c_{2} = 3 p_{g}$

Presentations for quaternionic $S$ -unit groups

Parametrizing Shimura subvarieties of $A_{1}$ Shimura varieties and related geometric problems

Cusp and $b_{1}$ growth for ball quotients and maps onto $Z$ with finitely generated kernel

Residually finite lattices in $PU (2, 1)$ and fundamental groups of smooth projective surfaces

A hyperbolic $4$ -orbifold with underlying space $P^{2}$

Classification and arithmeticity of toroidal compactifications with $3 c ˉ_{2} = c ˉ_{1}^{2} = 3$

Lattices in $PU (n, 1)$ that are not profinitely rigid

Residual finiteness for central extensions of lattices in $PU (n, 1)$ and negatively curved projective varieties