I-surfaces with one T-singularity

We classify normal stable surfaces with KX2=1, pg= 2 and q= 0 with a unique singular point which is a non-canonical T-singularity, thus exhibiting two divisors in the main component and a new irreducible component of the moduli space of stable surfaces M¯ 1 , 3

The Cohomologies of the Iwasawa Manifold and of Its Small Deformations

We prove that, for some classes of complex nilmanifolds, the Bott–Chern cohomology is completely determined by the Lie algebra associated with the nilmanifold with the induced complex structure. We use these tools to compute the Bott–Chern and Aeppli cohomologies of the Iwasawa manifold and of its small deformations, completing the computations by M. Schweitzer (arXiv:0709.3528v1 [math.AG])

Vertical–horizontal decomposition of Laplacians and cohomologies of manifolds with trivial tangent bundles

In this paper, we obtain a vertical–horizontal decomposition formula of Laplacians on manifolds with a special foliation structure. Two Nomizu-type theorems for cohomologies of nilmanifolds follow as applications

On the history of the Hopf problem

This short note serves as a historical introduction to the Hopf problem: "Does there exist a complex structure on S6?" This unsolved mathematical question was the subject of the Conference "MAM 1 12 (Non-)Existence of Complex Structures on S6", which took place at Philipps-Universit"at Marburg, Germany, between March 27th and March 30th, 2017

Open problems

A problem session, has been held during the workshop “Birational geometry of surfaces” which took place at the Department of Mathematics of the University of Rome “Tor Vergata”, in January, 11–15, 2016. In the following paper, we gather problems and questions that have been proposed and discussed during the event

Birational geometry of surfaces.

A problem session, has been held during the workshop “Birational geometry of surfaces” which took place at the Department of Mathematics of the University of Rome “Tor Vergata”, in January, 11–15, 2016. In the following paper, we gather problems and questions that have been proposed and discussed during the event