Zobrazeno 1 - 10
of 277
pro vyhledávání: '"Tomassini, Adriano"'
Autor:
Giudice, Ettore Lo, Tomassini, Adriano
Let $(M,J)$ be a $n$-dimensional complex manifold: a $p$-K\"ahler structure (resp. $p$-symplectic structure) on $M$ is a real, closed $(p,p)$-transverse form $\Omega$ (resp. real, closed $2p$-form whose $(p,p)$-component is transverse). We give obstr
Externí odkaz:
http://arxiv.org/abs/2407.11526
Autor:
Cattaneo, Andrea, Tomassini, Adriano
We provide families of compact $(n + 1)$-dimensional complex non K\"ahler manifolds satisfying the $\partial\bar{\partial}$-Lemma, with holomoprhically trivial canonical bundle, carrying a balanced metric and with no $p$-K\"ahler structures. Such a c
Externí odkaz:
http://arxiv.org/abs/2403.10126
Autor:
Sferruzza, Tommaso, Tomassini, Adriano
We study the interplay between geometrically-Bott-Chern-formal metrics and SKT metrics. We prove that a $6$-dimensional nilmanifold endowed with a invariant complex structure admits an SKT metric if and only if it is geometrically-Bott-Chern-formal.
Externí odkaz:
http://arxiv.org/abs/2402.02537
Autor:
Sillari, Lorenzo, Tomassini, Adriano
We study the spaces of $(d + d^c)$-harmonic forms and $(d + d^\Lambda)$-harmonic forms, the natural generalization of the spaces of Bott-Chern harmonic forms, resp. symplectic harmonic forms from complex, resp. symplectic, manifolds to almost Hermiti
Externí odkaz:
http://arxiv.org/abs/2310.10304
Let $(M,J)$ be a $2n$-dimensional almost complex manifold and let $x\in M$. We define the notion of almost complex blow-up of $(M,J)$ at $x$. We prove the existence of almost complex blow-ups at $x$ under suitable assumptions on the almost complex st
Externí odkaz:
http://arxiv.org/abs/2305.09825
Autor:
Sillari, Lorenzo, Tomassini, Adriano
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 operators $d$, $d^c$. We explain how they are connected to already existing c
Externí odkaz:
http://arxiv.org/abs/2303.17449
Autor:
Sillari, Lorenzo, Tomassini, Adriano
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 smooth functions on the underlying manifold solving a system of first or
Externí odkaz:
http://arxiv.org/abs/2211.08340
Let $(M^{2n},J)$ be a compact almost complex manifold. The almost complex invariant $h^{p,q}_J$ is defined as the complex dimension of the cohomology space $\left\{\left[\alpha\right]\in H^{p+q}_{dR}(M^{2n};\mathbb{C}) \,\vert\,\alpha\in A^{p,q}(M^{2
Externí odkaz:
http://arxiv.org/abs/2209.07286
We study the Kodaira dimension of a real parallelizable manifold $M$, with an almost complex structure $J$ in standard form with respect to a given parallelism. For $X = (M, J)$ we give conditions under which $\operatorname{kod}(X) = 0$. We provide e
Externí odkaz:
http://arxiv.org/abs/2207.04458
Autor:
Sferruzza, Tommaso, Tomassini, Adriano
We provide families of compact astheno-K\"ahler nilmanifolds and we study the behaviour of the complex blowup of such manifolds. We prove that the existence of an astheno-K\"ahler metric satisfying an extra differential condition is not preserved by
Externí odkaz:
http://arxiv.org/abs/2206.06904