175 research outputs found
Correnti positive: uno strumento per l'analisi globale su varietà complesse
No full textThis paper is a survey on positive currents on complex manifolds. It is essentially divided into two parts. In the first part the author
illustrates principal results on closed, positive currents: This is a very important class of currents
for complex manifolds because they are a natural generalization of submanifolds. In the second
part pluriharmonic and plurisubharmonic positive currents are illustrated; this class is important
because of the characterization of compact Kähler manifolds in terms of currents by Harvey and
Lawson. At the end of the paper an appendix, containing some preliminaries on the subject, helps
the nonexpert reader
On the Cohomology of a Holomorphically Separable Complex Analytic Space
No full textThe author gives the following extension of a result of M. Raimondo and A. Silva. Let X be a holomorphically separable complex
space (reduced and with countable topology) of dimension n ≥ 1, F a coherent analytic sheaf
on X and q a fixed integer > −codh F. Then if Hk(X; F) = 0 for all k > q, the vector space
Hq(X; F) is either zero or infinite-dimensional
p-Kähler Lie groups
No full textA complex Lie group G is left invariant p-Kähler if
it is p-Kähler and its p-Kähler form
is left invariant. A homogeneous space G/H is p-Kähler
if G is left invariant p-Kähler.
The author studies properties and examples of left invariant p-Kähler gruops, and moreover shows that given G/U compact and holomorphically
parallelizable, with U discrete, if G/U is p-Kähler then CN ×(G/U) is p-Kähler for any N ≥ 1
Product of generalized p-K\"ahler manifolds
No full textA product of K\"ahler manifolds also carries a K\"ahler metric. In this short note we would like to study the product of generalized p-K\"ahler 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-K\"ahler manifolds
A characterization of balanced manifolds
No full textA Hermitian metric on a complex manifold is Kähler if and only if it approximates the
Euclidean metric to order 2 at each point, in a suitable coordinate system. We prove here
an analogous characterization of balanced metrics, namely, a Hermitian metric is balanced
if and only if its fundamental form ω has closed trace and ωi, j (z) does not contain linear
terms involving zi , z j , \bar zi , \bar z j , for each point, in a suitable coordinate system
Classes of compact non-Kähler manifolds
No full text. We study various classes of compact non-Kähler manifolds, many of which already exist in the literature, which are characterized by positive forms and currents. The goal of the note is to present an overview that highlights the links between the various classes and raises some interesting problems
Forms and currents defining generalized p-Kaehler structures
No full textThis paper is devoted, first of all, to give a complete unified proof of the Characterization Theorem for compact generalized p-Kaehler manifolds.
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
Proper Modifications of Generalized p-Kähler Manifolds
No full textIn this paper, we consider a proper modification (Formula presented.) between complex manifolds, and study when a generalized p-Kähler property goes back from M to (Formula presented.). 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 (Formula presented.). For (Formula presented.), 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 also get some partial results in the non-compact case; finally, we end the paper with some examples of generalized p-Kähler manifolds
Geometria B
No full textCONTENUTO: Gruppi. Spazi vettoriali e applicazioni lineari. Diagonalizzazione. Forme bilineari, prodotti scalari, prodotti hermitiani. Superfici quadriche. Esercizi
Holomorphic submersions onto Kaehler or balanced manifolds
No full textWe study many properties concerning weak K\"ahlerianity on compact complex
manifolds which admits a holomorphic submersion onto a K\"ahler or a balanced
manifold. We get generalizations of some results of Harvey and Lawson (the
K\"ahler case), Michelson (the balanced case), Popovici (the SG case) and
others
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