(Bi-)Cohen-Macaulay simplicial complexes and their associated coherent sheaves
Algebraic Geometry
2011-12-14 v4 Combinatorics
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.
Cite
@article{arxiv.math/0209061,
title = {(Bi-)Cohen-Macaulay simplicial complexes and their associated coherent sheaves},
author = {Gunnar Floystad and Jon Eivind Vatne},
journal= {arXiv preprint arXiv:math/0209061},
year = {2011}
}
Comments
16 pages, some minor changes