n-blocks collections on Fano manifolds and sheaves with regularity −∞
Let X be a smooth Fano manifold equipped with a “ nice ” n-blocks collection in the sense of  and F a coherent sheaf on X . Assume that X is Fano and that all blocks are coherent sheaves. Here we prove that F has regularity −∞ in the sense of  if Supp(F) is finite, the converse being true under mild assumptions. The corresponding result is also true when X has a geometric collection in the sense of .
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