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

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

2002-09-06

arxiv.org/abs/math/0209061v4

Communications in Algebra 33, (2005), no.9, p. 3121-3136

Mathematics

Algebraic Geometry

16 pages, some minor changes

Scientific paper

10.1081/AGB-200066131

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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