(Bi-)Cohen-Macaulay simplicial complexes and their associated coherent sheaves
arXiv:math/0209061 · doi:10.1081/AGB-200066131
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.
16 pages, some minor changes