Subcanonical Graded Rings Which Are Not CohenMacaulay, with Appendix: A nonQGorenstein CohenMacaulay cone X with K_X QCartier
Abstract
The paper answers a question by Jonathan Wahl,giving examples of regular surfaces S (so their canonical ring is a Gorenstein graded ring) having the following properties: 1) their canonical divisor K_S = rL is a positive multiple of an ample divisor L 2) the graded ring R := R (X,L ) associated to L is not CohenMacaulay. In the appendix Wahl shows how these examples lead to the existence of CohenMacaulay singularities with K_X Q Cartier which are not Q Gorenstein, since their index one cover is not Cohen Macaulay.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.3815
 Bibcode:
 2014arXiv1402.3815C
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Commutative Algebra;
 14M05;
 14J29;
 13H10;
 32S20
 EPrint:
 To appear in a volume in honour of Rob Lazarsfeld's 60th birthday, London Mathematical Society Lecture Notes series (edited by Cambridge University Press)