5 papers
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.