Subcanonical Graded Rings Which Are Not Cohen-Macaulay, with Appendix: A non-Q-Gorenstein Cohen-Macaulay cone X with K_X Q-Cartier

2014/02/16 by Fabrizio Catanese, Catanese, Fabrizio, Appendix by Jonathan Wahl +1
Mathematics · #13H10 #14J29 #14M05 #32S20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1402.3815

openalex publication_date 2014/02/16 · openalex created_date 2016/09/16 · openalex updated_date 2026/07/28

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 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.

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