603 research outputs found
Hermitian structures on six dimensional nilmanifolds
Let (J,g) be a Hermitian structure on a compact nilmanifold M with invariant
complex structure J and compatible metric g, which is not required to be
invariant. We give classifications of 6-dimensional nilmanifolds M admitting
strong K\"ahler with torsion, balanced or locally conformal K\"ahler structures
(J,g).Comment: LaTeX, 24 pages, 1 figur
Symplectic harmonicity and generalized coeffective cohomologies
Relations between the symplectically harmonic cohomology and the coeffective
cohomology of a symplectic manifold are obtained. This is achieved through a
generalization of the latter, which in addition allows us to provide a
coeffective version of the filtered cohomologies introduced by C.-J. Tsai,
L.-S. Tseng and S.-T. Yau. We construct closed (simply connected) manifolds
endowed with a family of symplectic forms such that the dimensions
of these symplectic cohomology groups vary with respect to . A complete
study of these cohomologies is given for 6-dimensional symplectic nilmanifolds,
and concrete examples with special cohomological properties are obtained on an
-dimensional solvmanifold and on 2-step nilmanifolds in higher dimensions.Comment: 25 pages; revised version, new Theorem 5.7 and Section 8 added,
references update
On the Strominger system and holomorphic deformations
We show that the property of existence of solution to the Strominger system
in dimension six is neither open nor closed under holomorphic deformations of
the complex structure. These results are obtained both in the case of positive
slope parameter as well as in the case of negative slope parameter in the
anomaly cancellation equation
Six dimensional solvmanifolds with holomorphically trivial canonical bundle
We determine the 6-dimensional solvmanifolds admitting an invariant complex
structure with holomorphically trivial canonical bundle. Such complex
structures are classified up to isomorphism, and the existence of strong
K\"ahler with torsion (SKT), generalized Gauduchon, balanced and strongly
Gauduchon metrics is studied. As an application we construct a holomorphic
family of compact complex manifolds such that satisfies the
-Lemma and admits a balanced metric for any ,
but the central limit neither satisfies the -Lemma nor
admits balanced metrics.Comment: 32 pages; to appear in IMR
Weakly Lefschetz symplectic manifolds
The harmonic cohomology of a Donaldson symplectic submanifold and of an
Auroux symplectic submanifold are compared with that of its ambient space. We
also study symplectic manifolds satisfying a weakly Lefschetz property, that
is, the -Lefschetz propery. In particular, we consider the symplectic
blow-ups of the complex projective space along weakly Lefschetz symplectic
submanifolds. As an application we construct, for each even integer ,
compact symplectic manifolds which are -Lefschetz but not -Lefschetz.Comment: 22 pages; many improvements from previous versio
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