Subcanonical Graded Rings Which Are Not Cohen-Macaulay, with Appendix: A non-Q-Gorenstein Cohen-Macaulay cone X with K_X Q-Cartier
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 Cohen-Macaulay. In the appendix Wahl shows how these examples lead to the existence of Cohen-Macaulay singularities with K_X Q -Cartier which are not Q -Gorenstein, since their index one cover is not Cohen- Macaulay.
- Pub Date:
- February 2014
- Mathematics - Algebraic Geometry;
- Mathematics - Commutative Algebra;
- To appear in a volume in honour of Rob Lazarsfeld's 60-th birthday, London Mathematical Society Lecture Notes series (edited by Cambridge University Press)