New pseudo-effectivity theorems for relative canonical bundles and new algebraicity and uniruledness criteria for foliations on compact Kähler manifolds are established.
Properness criteria for families of coherent analytic sheaves
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abstract
We extend Langton's valuative criterion for families of coherent algebraic sheaves to a complex analytic set-up. As a consequence we derive a set of sufficient conditions for the compactness of a moduli space of semistable sheaves over a compact complex manifold. This applies also to some cases appearing in complex projective geometry not covered by previous results.
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Remarks on Relative Canonical Bundles and Algebraicity Criteria for Foliations in K\"ahler context
New pseudo-effectivity theorems for relative canonical bundles and new algebraicity and uniruledness criteria for foliations on compact Kähler manifolds are established.