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Abstract:We report on
I) small degree branched coverings of rational homogeneous spaces and,
II) small codimensional subvarieties of a Kaehler manifold with
semi-positive holomorphic bisectional curvature.
Even though these two problems are not equivalent, they share the need
to study the positivity of naturally associated vector bundles:
for I) one studies, with algebraic methods, the vector bundle associated
with the covering
for II) one studies, with algebraic and differential geometric methods,
the tangent bundle.
Strong topological restrictions on the covering space follow and they are called Barth-type theorems in
the literature.
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