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On the supports for cohomology classes of complex manifolds
Portelli, Dario
2012
Abstract
Let $X$ be a compact, connected complex manifold, and let
$\xi\in H^{i}(X,{\mathbb Q} )$ be a non-trivial class. The paper
deals with the possibility to construct a topological cycle $\Gamma$ on $X,$ whose
class is the Poincar\'e dual of $\xi\thinspace ,$ which is closely related
in a precise sense to the complex structure of $X.$ The desired properties of $\Gamma$ allow
to define a differentiable relation into a suitable space of $1$-jets.
This relation shows that there is a preliminary topological obstruction to
construct such a $\Gamma$.
The main result of the paper is that, in a relevant particular case, this
obstruction disappears.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
44 (2012)
Publisher
EUT Edizioni Università di Trieste
Source
Dario Portelli, "Dedicated On the supports for cohomology classes of complex manifolds", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 44 (2012), pp. 349–369.
Languages
en
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