16 citations · 32 across the 17 of their papers we have counts for
28 papers
Almgren frequency and Agmon convexity on rotationally symmetric Cartan-Hadamard manifolds
Luca F. Di Cerbo
We introduce a \emph{global} frequency function for harmonic functions on rotationally symmetric Cartan-Hadamard manifolds. In real hyperbolic space, we also identify a different f…
Aspherical Complex Surfaces, the Singer Conjecture, and Gromov-Lück Inequality
Michael Albanese, Luca F. Di Cerbo, Luigi Lombardi
We discuss the Singer conjecture and Gromov-Lück inequality for aspherical complex surfaces. We give a proof of the Singer conjecture for aspherical complex surface wit…
On the Hopf Problem and a Conjecture of Liu-Maxim-Wang
Luca F. Di Cerbo, Rita Pardini
We discuss an approach towards the Hopf problem for aspherical smooth projective varieties recently proposed by Liu, Maxim, and Wang in [LMW21]. In complex dimension two, we point…
The signature of geometrically decomposable aspherical 4-manifolds
Luca Fabrizio Di Cerbo, Marco Golla
We construct examples of geometrically decomposable aspherical 4-manifolds with non-zero signature. We show that all such 4-manifolds satisfy the inequality (of Bogomolov--Miyaoka-…
Aspherical 4-Manifolds, Complex Structures, and Einstein Metrics
Michael Albanese, Luca F. Di Cerbo
We show that extended graph 4-manifolds with positive Euler characteristic cannot support a complex structure. This result stems from a new proof of the fact that a closed real-hyp…
Singer Conjecture for Varieties with Semismall Albanese Map and Residually Finite Fundamental Group
Luca F. Di Cerbo, Luigi Lombardi
We prove the Singer conjecture for varieties with semismall Albanese map and residually finite fundamental group.
On the impossibility of four-dimensional complex-hyperbolic Einstein Dehn filling
Luca F. Di Cerbo, Marco Golla
We show that the complex-hyperbolic Einstein Dehn filling compactification cannot possibly be performed in dimension four.
Generalized Graph Manifolds, Residual Finiteness, and the Singer Conjecture
Luca F. Di Cerbo, Michael Hull
We prove the Singer conjecture for extended graph manifolds and pure complex-hyperbolic higher graph manifolds with residually finite fundamental groups. In real dimension three, w…
On the Betti Numbers of Finite Volume Hyperbolic Manifolds
Luca F. Di Cerbo, Mark Stern
We obtain strong upper bounds for the Betti numbers of compact complex-hyperbolic manifolds. We use the unitary holonomy to improve the results given by the most direct application…
Harmonic Forms, Price Inequalities, and Benjamini-Schramm Convergence
Luca F. Di Cerbo, Mark Stern
We study Betti numbers of sequences of Riemannian manifolds which Benjamini-Schramm converge to their universal covers. Using the Price inequalities we developed elsewhere, we deri…
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 . For example, we show that smooth toroidal compactifications of ball quotients…
Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points
Luca F. Di Cerbo, Mark Stern
We derive Price inequalities for harmonic forms on manifolds without conjugate points and with a negative Ricci upper bound. The techniques employed in the proof work particularly…
Exceptional collections and the bicanonical map of Keum's fake projective planes
Gennaro Di Brino, Luca F. Di Cerbo
We apply the recent results of Galkin et al. [GKMS15] to study some geometrical features of Keum's fake projective planes. Among other things, we show that the bicanonical map of K…
The Toledo invariant, and Seshadri constants of fake projective planes
Luca F. Di Cerbo
The purpose of this paper is to explicitly compute the Seshadri constants of all ample line bundles on fake projective planes. The proof relies on the theory of the Toledo invarian…
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…
Classification and arithmeticity of toroidal compactifications with
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…
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 can be realized as a smooth toroidal compactification of a ball quotient. It follows from work of Hirz…
On the canonical divisor of smooth toroidal compactifications
Gabriele Di Cerbo, Luca F. Di Cerbo
In this paper, we show that the canonical divisor of a smooth toroidal compactification of a complex hyperbolic manifold must be nef if the dimension is greater or equal to three.…
On Seshadri constants of varieties with large fundamental group
Gabriele Di Cerbo, Luca F. Di Cerbo
Let be a smooth variety and let be an ample line bundle on . If is large, we show that the Seshadri constant can be made arbitrarily large b…
A sharp cusp count for complex hyperbolic surfaces and related results
Gabriele Di Cerbo, Luca Fabrizio Di Cerbo
We derive a sharp cusp count for finite volume complex hyperbolic surfaces which admit smooth toroidal compactifications. We use this result, and the techniques developed in [DiC12…
On the classification of toroidal compactifications with and
Luca Fabrizio Di Cerbo
We classify the smallest finite volume complex hyperbolic surfaces with cusps which admit smooth toroidal compactifications and which are not birational to a bi-elliptic surface. R…
Effective results for complex hyperbolic manifolds
Gabriele Di Cerbo, Luca F. Di Cerbo
The goal of this paper is to study the geometry of cusped complex hyperbolic manifolds through their compactifications. We characterize toroidal compactifications with non-nef cano…
Positivity in Kähler-Einstein theory
Gabriele Di Cerbo, Luca F. Di Cerbo
Tian initiated the study of incomplete Kähler-Einstein metrics on quasi-projective varieties with cone-edge type singularities along a divisor, described by the cone-angle $2π(1-α)…
On Kähler-Einstein surfaces with edge singularities
Luca Fabrizio Di Cerbo
In this paper we characterize logarithmic surfaces which admit Kähler-Einstein metrics with negative scalar curvature and small edge singularities along a normal crossing divisor.