Nicoletta Tardini

activity

20152026

most citedNote on Dolbeault cohomology and Hodge structures up to bimeromorphisms

22 citations · 69 across the 22 of their papers we have counts for

collaborators

27 papers

math.DG2026

Cohomological properties and Hermitian metrics of complex non-Kähler manifolds

Daniele Angella, Nicoletta Tardini

We give a partial account of some problems concerning cohomological invariants and metric properties of complex non-Kähler manifolds.

math.DG2025

$\del\delbar$-Lemma and Bott-Chern cohomology of twistor spaces

Anna Fino, Gueo Grantcharov, Nicoletta Tardini +2

In the paper we study the Bott-Chern and Aeppli cohomologies of the twistor space of a compact self-dual 4-manifold and we characterize the validity of the $\partial \overline \par…

math.DG2025

Complex symplectic structures: deformations and cohomology

Giovanni Bazzoni, Marco Freibert, Adela Latorre +1

We show that complex symplectic structures need not be preserved under small deformations, and we find sufficient conditions for this to happen. We study various cohomologies of co…

math.DG2024

The pluriclosed flow and the Vaisman condition

Giuseppe Barbaro, Francesco Pediconi, Nicoletta Tardini

We prove that the pluriclosed flow preserves the Vaisman condition on compact complex surfaces if and only if the starting metric has constant scalar curvature.

math.DG2024

Pluriclosed manifolds with parallel Bismut torsion

Giuseppe Barbaro, Francesco Pediconi, Nicoletta Tardini

We present a complete classification of simply-connected pluriclosed manifolds with parallel Bismut torsion, extending previously known results in the literature. Consequently, we…

math.DG2023

Projectively induced Kähler cones over regular Sasakian manifolds

Stefano Marini, Nicoletta Tardini, Michela Zedda

Motivated by a conjecture in [9] we prove that the Kähler cone over a regular complete Sasakian manifold is Ricci-flat and projectively induced if and only if it is flat. We also o…

math.DG2023

On the invariant and anti-invariant cohomologies of hypercomplex manifolds

Mehdi Lejmi, Nicoletta Tardini

A hypercomplex structure $(I, J, K)$ on a manifold $M$ is said to be $C^{\infty}$ -pure-and-full if the Dolbeault cohomology $H_{\partial}^{2, 0} (M, I)$ is the direct sum of two natural s…

math.DG2022★ 2 cited

Complex Symplectic Lie Algebras with Large Abelian Subalgebras

Giovanni Bazzoni, Marco Freibert, Adela Latorre +1

We present two constructions of complex symplectic structures on Lie algebras with large abelian ideals. In particular, we completely classify complex symplectic structures on almo…

math.DG2022

HKT manifolds: Hodge theory, formality and balanced metrics

Giovanni Gentili, Nicoletta Tardini

Let $(M, I, J, K, Ω)$ be a compact HKT manifold and denote with $\partial$ the conjugate Dolbeault operator with respect to $I$ , $\partial_{J} := J^{- 1} \partial J$ , $\partial^Λ:=[…

math.DG2022

An integral condition involving $\partial$ -harmonic $(0, 1)$ -forms

Anna Fino, Nicoletta Tardini, Adriano Tomassini

We study compact almost complex manifolds admitting a Hermitian metric satisfying an integral condition involving $\partial$ -harmonic $(0, 1)$ -forms. We prove that this in…

math.DG2022★ 3 cited

Bott-Chern harmonic forms and primitive decompositions on compact almost Kähler manifolds

Riccardo Piovani, Nicoletta Tardini

Let $(X, J, ω)$ be a compact $2 n$ -dimensional almost Kähler manifold. We prove primitive decompositions for Bott-Chern and Aeppli harmonic forms in special bidegrees and show that su…

math.DG2022★ 2 cited

Primitive decompositions of Dolbeault harmonic forms on compact almost-Kähler manifolds

Andrea Cattaneo, Nicoletta Tardini, Adriano Tomassini

Let $(X, J, g, ω)$ be a compact $2 n$ -dimensional almost-Kähler manifold. We prove primitive decompositions of $\partial$ -, $\partial$ -harmonic forms on $X$ in bidegree $(1,…

math.DG2021

$p$ -Kähler and balanced structures on nilmanifolds with nilpotent complex structures

Tommaso Sferruzza, Nicoletta Tardini

Let $(X, J)$ be a nilmanifold with a left-invariant nilpotent complex structure. We study the existence of $p$ -Kähler structures (which include Kähler and balanced metrics) on $X$ .…

math.DG2021

Almost-complex invariants of families of six-dimensional solvmanifolds

Nicoletta Tardini, Adriano Tomassini

We compute almost-complex invariants $h_{\partial}^{p, 0}$ , $h_{Dol}^{p, 0}$ and almost-Hermitian invariants $h_{δ ˉ}^{p, 0}$ on families of almost-Kähler and almost…

math.DG2021★ 4 cited

$\partial$ -Harmonic forms on $4$ -dimensional almost-Hermitian manifolds

Nicoletta Tardini, Adriano Tomassini

Let $(X, J)$ be a $4$ -dimensional compact almost-complex manifold and let $g$ be a Hermitian metric on $(X, J)$ . Denote by $Δ_{\overline\partial}:=\overline\partial\overline\partial^…

math.DG2021★ 1 cited

Pluriclosed and Strominger Kähler-like metrics compatible with abelian complex structures

Anna Fino, Nicoletta Tardini, Luigi Vezzoni

We show that the existence of a left-invariant pluriclosed Hermitian metric on a unimodular Lie group with a left-invariant abelian complex structure forces the group to be $2$ -ste…

math.DG2020

Some remarks on Hermitian manifolds satisfying Kähler-like conditions

Anna Fino, Nicoletta Tardini

We study Hermitian metrics whose Bismut connection $\nabla^{B}$ satisfies the first Bianchi identity in relation to the SKT condition and the parallelism of the torsion of the Bimut…

math.DG2019

Differential operators on almost-Hermitian manifolds and harmonic forms

Nicoletta Tardini, Adriano Tomassini

We consider several differential operators on compact almost-complex, almost-Hermitian and almost-Kähler manifolds. We discuss Hodge Theory for these operators and a possible cohom…

math.DG2019★ 7 cited

Variational problems in conformal geometry

Daniele Angella, Nicolina Istrati, Alexandra Otiman +1

We study the Euler-Lagrange equation for several natural functionals defined on a conformal class of almost Hermitian metrics, whose expression involves the Lee form $θ$ of the met…

math.DG2018★ 1 cited

Relative Čech-Dolbeault homology and applications

Nicoletta Tardini

We define the relative Dolbeault homology of a complex manifold with currents via a Čech approach and we prove its equivalence with the relative Čech-Dolbeault cohomology as define…

math.SG2018★ 3 cited

Symplectic cohomologies and deformations

Nicoletta Tardini, Adriano Tomassini

In this note we study the behavior of symplectic cohomology groups under symplectic deformations. Moreover, we show that for compact almost-Kähler manifolds $(X, J, g, ω)$ with $J$ $\…

math.DG2017★ 22 cited

Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms

Daniele Angella, Tatsuo Suwa, Nicoletta Tardini +1

We construct a simply-connected compact complex non-Kähler manifold satisfying the $\partial \partial ˉ$ -Lemma, and endowed with a balanced metric. To this aim, we were initially…

math.DG2017★ 5 cited

Cohomologies of locally conformally symplectic manifolds and solvmanifolds

Daniele Angella, Alexandra Otiman, Nicoletta Tardini

We study the Morse-Novikov cohomology and its almost-symplectic counterpart on manifolds admitting locally conformally symplectic structures. More precisely, we introduce lcs cohom…

math.DG2016

Cohomological aspects on complex and symplectic manifolds

Nicoletta Tardini

We discuss how quantitative cohomological informations could provide qualitative properties on complex and symplectic manifolds. In particular we focus on the Bott-Chern and the Ae…

Cohomological properties and Hermitian metrics of complex non-Kähler manifolds

$\del\delbar$-Lemma and Bott-Chern cohomology of twistor spaces

Complex symplectic structures: deformations and cohomology

The pluriclosed flow and the Vaisman condition

Pluriclosed manifolds with parallel Bismut torsion

Projectively induced Kähler cones over regular Sasakian manifolds

On the invariant and anti-invariant cohomologies of hypercomplex manifolds

Complex Symplectic Lie Algebras with Large Abelian Subalgebras

HKT manifolds: Hodge theory, formality and balanced metrics

An integral condition involving ∂-harmonic (0,1)-forms

Bott-Chern harmonic forms and primitive decompositions on compact almost Kähler manifolds

Primitive decompositions of Dolbeault harmonic forms on compact almost-Kähler manifolds

p-Kähler and balanced structures on nilmanifolds with nilpotent complex structures

Almost-complex invariants of families of six-dimensional solvmanifolds

∂-Harmonic forms on 4-dimensional almost-Hermitian manifolds

Pluriclosed and Strominger Kähler-like metrics compatible with abelian complex structures

Some remarks on Hermitian manifolds satisfying Kähler-like conditions

Differential operators on almost-Hermitian manifolds and harmonic forms

Variational problems in conformal geometry

Relative Čech-Dolbeault homology and applications

Symplectic cohomologies and deformations

Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms

Cohomologies of locally conformally symplectic manifolds and solvmanifolds

Cohomological aspects on complex and symplectic manifolds

An integral condition involving $\partial$ -harmonic $(0, 1)$ -forms

$p$ -Kähler and balanced structures on nilmanifolds with nilpotent complex structures

$\partial$ -Harmonic forms on $4$ -dimensional almost-Hermitian manifolds