Weak forms of $\ddb-$Lemma on compact complex manifolds
This paper is devoted to give a complete unified study of several weak forms of $\ddb-$Lemma on compact complex manifolds.
math.DG↗
arXiv subjects
Lucia Alessandrini
Publications and source records attributed to Lucia Alessandrini.
Forms and currents defining generalized $p-$Kähler structures
This paper is devoted, first of all, to give a complete unified proof of the Characterization Theorem for compact generalized $p-$Kähler manifolds (Theorem 3.2). The proof is based on the classical duality between "closed" positive forms and "exact" positive currents. In the last part of the paper we approach the general case of non compact complex manifolds, where "exact" positive forms seem to play a more significant role than "closed" forms. In this setting, we state the appropriate characterization theorems and give some interesting applications.
math.DG↗
Product of generalized $p-$Kähler manifolds
A product of Kähler manifolds also carries a Kähler metric. In this short note we would like to study the product of generalized $p-$Kähler manifolds, compact or not. The results we get extend the known results (balanced, SKT, sG manifolds), and are optimal in the compact case. Hence we can give new non-trivial examples of generalized $p-$Kähler manifolds.
math.DG↗
Holomorphic submersions onto Kähler or balanced manifolds
We study many properties concerning weak Kählerianity on compact complex manifolds which admits a holomorphic submersion onto a Kähler or a balanced manifold. We get generalizations of some results of Harvey and Lawson (the Kähler case), Michelson (the balanced case), Popovici (the sG case) and others.
math.DG↗
Proper modifications of generalized $p-$Kähler manifolds
In this paper, we consider a proper modification $f : \tilde M \to M$ between complex manifolds, and study when a generalized $p-$Kähler property goes back from $M$ to $\tilde M$. When $f$ is the blow-up at a point, every generalized $p-$Kähler property is conserved, while when $f$ is the blow-up along a submanifold, the same is true for $p=1$. For $p=n-1$, we prove that the class of compact generalized balanced manifolds is closed with respect to modifications, and we show that the fundamental forms can be chosen in the expected cohomology class. We get some partial results also in the non-compact case; finally, we end the paper with some examples of generalized $p-$Kähler manifolds.
math.DG↗