Positivity notions for coherent sheaves over compact complex spaces |
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Authors: | Joshua H Rabinowitz |
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Institution: | (1) Department of Mathematics, University of Illinois at Chicago Circle, 60680 Chicago, IL, USA |
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Abstract: | LetX be a reduced compact complex space, ![oS](/content/x4xjk48752721771/xxlarge9416.gif) X a coherent sheaf, andV=V( ) its associated linear fiber space. LetV
R
be the reduction ofV, letA be the analytic set inX over which is not locally-free, and letV be the closure inV
R
ofV
R
|(X–A). is (primary) weakly positive if the zerosection ofV (V ) is exceptional. is (primary) cohomologically positive if, for any coherent sheaf ![daleth](/content/x4xjk48752721771/xxlarge8504.gif) X, for all ![mgr](/content/x4xjk48752721771/xxlarge956.gif) 0,k 1. Then is (primary) weakly positive if and only if is (primary) cohomologically positive.LetX be a normal irreducible compact complex space. ThenX is Moishezon if and only if it carries a primary weakly positive, and hence primary cohomologically positive, coherent sheaf.Several other positivity notions are also discussed. |
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Keywords: | |
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