7 citations · 7 across the 10 of their papers we have counts for
11 papers
Non-trivial ABC-Massey products on complex parallelisable solvmanifolds
Nunzia Cesarino, Tommaso Sferruzza, Adriano Tomassini
Triple Aeppli--Bott--Chern--Massey products, shortly, triple ABC-Massey products are higher-order operations on the Bott--Chern and Aeppli cohomologies of a compact complex manifol…
Dolbeault formality for complex nilmanifolds
Tommaso Sferruzza, Misha Verbitsky
A quasi-isomorphism of differential graded algebras (DGA) is a multiplicative map inducing an isomorphism on cohomology. A DGA is called formal if it can be connected by a chain of…
Hermitian geometrically formal manifolds
Tommaso Sferruzza, Adriano Tomassini
We study Hermitian geometrically formal metrics on compact complex manifolds, focusing on Dolbeault, Bott-Chern, and Aeppli cohomologies. We establish topological and cohomological…
Bott-Chern formality and Massey products on strong Kähler with torsion and Kähler solvmanifolds
Tommaso Sferruzza, Adriano Tomassini
We study the interplay between geometrically-Bott-Chern-formal metrics and SKT metrics. We prove that a -dimensional nilmanifold endowed with a invariant complex structure admit…
Almost complex blow-ups and positive closed -forms on -dimensional almost complex manifolds
Richard Hind, Tommaso Sferruzza, Adriano Tomassini
Let be a -dimensional almost complex manifold and let . We define the notion of almost complex blow-up of at . We prove the existence of almost compl…
Deformations of astheno-Kähler metrics
Tommaso Sferruzza
The property of admitting an astheno-Kähler metric is not stable under the action of small deformations of the complex structure of a compact complex manifold. In this paper, we pr…
On cohomological and formal properties of Strong Kähler with torsion and astheno-Kähler metrics
Tommaso Sferruzza, Adriano Tomassini
We provide families of compact astheno-Kähler nilmanifolds and we study the behaviour of the complex blowup of such manifolds. We prove that the existence of an astheno-Kähler metr…
Dolbeault and Bott-Chern formalities: deformations and -lemma
Tommaso Sferruzza, Adriano Tomassini
It is proved that the properties of being Dolbeault formal and geometrically-Bott-Chern-formal are not closed under holomorphic deformations of the complex structure. Further, we c…
-Kähler and balanced structures on nilmanifolds with nilpotent complex structures
Tommaso Sferruzza, Nicoletta Tardini
Let be a nilmanifold with a left-invariant nilpotent complex structure. We study the existence of -Kähler structures (which include Kähler and balanced metrics) on .…
Deformations of balanced metrics
Tommaso Sferruzza
Small deformations of the complex structure do not always preserve special metric properties in the Hermitian non-Kähler setting. In this paper, we find necessary conditions for th…
Deformations of Strong Kähler with torsion metrics
Riccardo Piovani, Tommaso Sferruzza
Existence of strong Kähler with torsion metrics, shortly SKT metrics, on complex manifolds has been shown to be unstable under small deformations. We find necessary conditions unde…