(Bi-)Cohen-Macaulay simplicial complexes and their associated coherent sheaves
Abstract
Via the BGG correspondence a simplicial complex Delta on [n] is transformed into a complex of coherent sheaves on Pn-1. We show that this complex reduces to a coherent sheaf F exactly when the Alexander dual Delta* is Cohen-Macaulay. We then determine when both Delta and Delta* are Cohen-Macaulay. This corresponds to F being a locally Cohen-Macaulay sheaf. Lastly we conjecture for which range of invariants of such Delta it must be a cone.
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