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Some projective surfaces of GK-dimension 4
| Content Provider | Scilit |
|---|---|
| Author | Rogalski, D. Sierra, Susan J. |
| Copyright Year | 2012 |
| Description | Journal: Compositio Mathematica We construct an interesting family of connected graded domains of Gel’fand–Kirillov dimension 4, and show that the general member of this family is noetherian. The algebras we construct are Koszul and have global dimension 4. They fail to be Artin–Schelter Gorenstein, however, showing that a theorem of Zhang and Stephenson for dimension 3 algebras does not extend to dimension 4. The Auslander–Buchsbaum formula also fails to hold for these algebras. The algebras we construct are birational to $ℙ^{2}$, and their existence disproves a conjecture of the first author and Stafford. The algebras can be obtained as global sections of a certain quasicoherent graded sheaf on $ℙ^{1}×ℙ^{1}$, and our key technique is to work with this sheaf. In contrast to all previously known examples of birationally commutative graded domains, the graded pieces of the sheaf fail to be ample in the sense of Van den Bergh. Our results thus require significantly new techniques. |
| Ending Page | 1237 |
| Starting Page | 1195 |
| ISSN | 00221295 |
| e-ISSN | 15705846 |
| DOI | 10.1112/s0010437x12000188 |
| Journal | Compositio Mathematica |
| Issue Number | 4 |
| Volume Number | 148 |
| Language | English |
| Publisher | Wiley-Blackwell |
| Publisher Date | 2012-07-01 |
| Access Restriction | Open |
| Subject Keyword | Journal: Compositio Mathematica Graded Domains Algebras We Construct |
| Content Type | Text |
| Resource Type | Article |
| Subject | Algebra and Number Theory |
