1,864 research outputs found
Group actions, non-K\"ahler complex manifolds and SKT structures
We give a construction of integrable complex structures on the total space of
a smooth principal bundle over a complex manifold, with an even dimensional
compact Lie group as structure group, under certain conditions. This
generalizes the constructions of complex structure on compact Lie groups by
Samelson and Wang, and on principal torus bundles by Calabi-Eckmann and others.
It also yields large classes of new examples of non-K\"ahler compact complex
manifolds. Moreover, under suitable restrictions on the base manifold, the
structure group, and characteristic classes, the total space of the principal
bundle admits SKT metrics. This generalizes recent results of Grantcharov et
al. We study the Picard group and the algebraic dimension of the total space in
some cases. We also use a slightly generalized version of the construction to
obtain (non-K\"ahler) complex structures on tangential frame bundles of complex
orbifolds.Comment: A new Section 4 is adde
The Toledo invariant on smooth varieties of general type
We propose a definition of the Toledo invariant for representations of
fundamental groups of smooth varieties of general type into semisimple Lie
groups of Hermitian type. This definition allows to generalize the results
known in the classical case of representations of complex hyperbolic lattices
to this new setting: assuming that the rank of the target Lie group is not
greater than two, we prove that the Toledo invariant satisfies a Milnor-Wood
type inequality and we characterize the corresponding maximal representations.Comment: 19 page
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