6 citations · 17 across the 14 of their papers we have counts for
14 papers
Invariant forms compute the Dolbeault cohomology of complex nilmanifolds
Keizo Hasegawa, Lorenzo Sillari, Adriano Tomassini
We prove that the inclusion of left-invariant forms into the Dolbeault complex of a compact nilmanifold endowed with a left-invariant complex structure induces an isomorphi…
Biholomorphism type of left-invariant complex structures on nilpotent Lie groups
Keizo Hasegawa, Sönke Rollenske, Lorenzo Sillari +2
In this note we prove a conjecture by Hasegawa stating that a simply connected, nilpotent Lie group of dimension endowed with a left-invariant complex structure is biholomorph…
Classification of homogeneous almost complex -manifolds with non-degenerate torsion bundle
Cristina Bozzetti, Costantino Medori, Lorenzo Sillari
We investigate the local and global geometry of almost complex -manifolds admitting non-degenerate torsion bundle. The rigidity of these structures forces a parallelizable -a…
Kodaira dimension of almost complex -manifolds with torsion first Chern class
Lorenzo Sillari, Adriano Tomassini
In this paper we investigate the Kodaira dimension of almost complex -manifolds with torsion first Chern class. First, we prove that, if the almost complex structure is also tam…
Kodaira dimension of -structures
Lorenzo Sillari, Adriano Tomassini
We study the Kodaira dimension of almost complex manifolds admitting an -structure. We introduce the notion of almost complex structure of splitting type and of as…
Invariant and non-invariant almost complex structures on compact quotients of Lie groups
Lorenzo Sillari, Adriano Tomassini
In this paper we briefly survey the classical problem of understanding which Lie algebras admit a complex structure, put in the broader perspective of almost complex structures wit…
Real analytic curves of almost complex structures
Lorenzo Sillari
We prove that, on a compact almost complex manifold, the space of almost complex structures whose Nijenhuis tensor has rank at least at every point is either empty or dense in…
On the Kodaira-Spencer's problem on almost Hermitian -manifolds
L. Sillari, A. Tomassini
In 1954, Hirzebruch reported a problem posed by Kodaira and Spencer: on compact almost complex manifolds, is the dimension of the kernel of the Dolbeault…
On the spaces of -harmonic forms and -harmonic forms on almost Hermitian manifolds and complex surfaces
Lorenzo Sillari, Adriano Tomassini
We study the spaces of -harmonic forms and -harmonic forms, the natural generalization of the spaces of Bott-Chern harmonic forms, resp. symplectic harmonic f…
On Bott-Chern and Aeppli cohomologies of almost complex manifolds and related spaces of harmonic forms
Lorenzo Sillari, Adriano Tomassini
In this paper we introduce several new cohomologies of almost complex manifolds, among which stands a generalization of Bott-Chern and Aeppli cohomologies defined using the operato…
Rank of the Nijenhuis tensor on parallelizable almost complex manifolds
Lorenzo Sillari, Adriano Tomassini
We study almost complex structures on parallelizable manifolds via the rank of their Nijenhuis tensor. First, we show how the computations of such rank can be reduced to finding sm…
Generalized Luttinger surgery and other cut-and-paste constructions in generalized complex geometry
Lorenzo Sillari
Exploiting the affinity between stable generalized complex structures and symplectic structures, we explain how certain constructions coming from symplectic geometry can be perform…
On the minimal number of solutions of the equation , ,
Matteo Ferrari, Lorenzo Sillari
We fix a positive integer and look for solutions of the equations and . We prove that Fermat primes can be used to build five solutions for th…
Dolbeault and -invariant cohomologies on almost complex manifolds
Lorenzo Sillari, Adriano Tomassini
In this paper we relate the cohomology of -invariant forms to the Dolbeault cohomology of an almost complex manifold. We find necessary and sufficient condition for the inclusio…