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(Bi-)Cohen-Macaulay simplicial complexes and their associated coherent sheaves

Gunnar Floystad·Jon Eivind Vatne
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Abstract

Via the BGG correspondence a simplicial complex Delta on [n] is transformed into a complex of coherent sheaves on P^n-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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Gunnar Floystad, Jon Eivind Vatne. 2004-01-20. (Bi-)Cohen-Macaulay simplicial complexes and their associated coherent sheaves. https://doi.org/10.1081/agb-200066131

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