15 research outputs found
(Bi-)Cohen-Macaulay simplicial complexes and their associated coherent sheaves
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.Comment: 16 pages, some minor change
PBW-deformations of N-Koszul algebras
For a quotient algebra of the tensor algebra we give explicit conditions
on its relations for being a PBW-deformation of an -Koszul algebra .
We show there is a one-one correspondence between such deformations and a class
of -structures on the Yoneda algebra of . We
compute the PBW-deformations of the algebra whose relations are the
anti-symmetrizers of degree and also of cubic Artin-Schelter algebras.Comment: 35 pages. Some minor correction