Riccardo Piovani

activity

20182024

most citedOn the dimension of Dolbeault harmonic (1,1)-forms on almost Hermitian 4-manifolds

7 citations · 16 across the 9 of their papers we have counts for

collaborators

11 papers

math.DG2024

On the cohomology of the Bigolin complex

Riccardo Piovani

Given a compact complex manifold, we study the cohomology and the Hodge theory for the elliptic complex of differential forms defined by Bigolin in 1969 and recently referred to as…

math.DG2023

Left-invariant almost complex structures on the higher dimensional Kodaira-Thurston manifolds

Tom Holt, Riccardo Piovani

We develop computational techniques which allow us to calculate the Kodaira dimension as well as the dimension of spaces of Dolbeault harmonic forms for left-invariant almost compl…

math.CV2023

The $L^{2}$ Aeppli-Bott-Chern Hilbert complex

Tom Holt, Riccardo Piovani

We analyse the $L^{2}$ Hilbert complexes naturally associated to a non-compact complex manifold, namely the ones which originate from the Dolbeault and the Aeppli-Bott-Chern complexe…

math.DG2022★ 1 cited

Invariants of almost complex and almost Kähler manifolds

Tom Holt, Riccardo Piovani, Adriano Tomassini

Let $(M^{2 n}, J)$ be a compact almost complex manifold. The almost complex invariant $h_{J}^{p, q}$ is defined as the complex dimension of the cohomology space $\left\{\left[α\right]\i…

math.DG2022

Primitive decomposition of Bott-Chern and Dolbeault harmonic $(k, k)$ -forms on compact almost Kähler manifolds

Tom Holt, Riccardo Piovani

We consider the primitive decomposition of $\partial ˉ, \partial$ , Bott-Chern and Aeppli-harmonic $(k, k)$ -forms on compact almost Kähler manifolds $(M, J, ω)$ . For any $D \in \{\b…

math.DG2022★ 4 cited

Dolbeault Harmonic $(1, 1)$ -forms on $4$ -dimensional compact quotients of Lie Groups with a left invariant almost Hermitian structure

Riccardo Piovani

We study Dolbeault harmonic $(1, 1)$ -forms on compact quotients $M = Γ\ G$ of $4$ -dimensional Lie groups $G$ admitting a left invariant almost Hermitian structure $(J, ω)$ . 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★ 7 cited

On the dimension of Dolbeault harmonic (1,1)-forms on almost Hermitian 4-manifolds

Riccardo Piovani, Adriano Tomassini

We prove that the dimension $h_{\partial}^{1, 1}$ of the space of Dolbeault harmonic $(1, 1)$ -forms is not necessarily always equal to $b^{-}$ on a compact almost complex 4-ma…

math.DG2021★ 1 cited

Bott-Chern Laplacian on almost Hermitian manifolds

Riccardo Piovani, Adriano Tomassini

Let $(M, J, g, ω)$ be a $2 n$ -dimensional almost Hermitian manifold. We extend the definition of the Bott-Chern Laplacian on $(M, J, g, ω)$ , proving that it is still elliptic. On a compac…

math.DG2019

Aeppli cohomology and Gauduchon metrics

Riccardo Piovani, Adriano Tomassini

Let $(M, J, g, ω)$ be a complete Hermitian manifold of complex dimension $n \geq 2$ . Let $1 \leq p \leq n - 1$ and assume that $ω^{n - p}$ is $(\partial + \partial)$ -bounded. We prove t…

math.CV2018

Bott-Chern Harmonic Forms on Stein Manifolds

Riccardo Piovani, Adriano Tomassini

Let $M$ be an $n$ -dimensional $d$ -bounded Stein manifold $M$ , i.e., a complex $n$ -dimensional manifold $M$ admitting a smooth strictly plurisubharmonic exhaustion $ρ$ and endowed w…

On the cohomology of the Bigolin complex

Left-invariant almost complex structures on the higher dimensional Kodaira-Thurston manifolds

The L2 Aeppli-Bott-Chern Hilbert complex

Invariants of almost complex and almost Kähler manifolds

Primitive decomposition of Bott-Chern and Dolbeault harmonic (k,k)-forms on compact almost Kähler manifolds

Dolbeault Harmonic (1,1)-forms on 4-dimensional compact quotients of Lie Groups with a left invariant almost Hermitian structure

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

On the dimension of Dolbeault harmonic (1,1)-forms on almost Hermitian 4-manifolds

Bott-Chern Laplacian on almost Hermitian manifolds

Aeppli cohomology and Gauduchon metrics

Bott-Chern Harmonic Forms on Stein Manifolds

The $L^{2}$ Aeppli-Bott-Chern Hilbert complex

Primitive decomposition of Bott-Chern and Dolbeault harmonic $(k, k)$ -forms on compact almost Kähler manifolds

Dolbeault Harmonic $(1, 1)$ -forms on $4$ -dimensional compact quotients of Lie Groups with a left invariant almost Hermitian structure