A family of local rings with rational Poincaré series
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- by Juan Elias and Giuseppe Valla PDF
- Proc. Amer. Math. Soc. 137 (2009), 1175-1178 Request permission
Abstract:
In this note we compute the Poincaré series of almost stretched Gorenstein local rings. It turns out that it is rational.References
- Shreeram Shankar Abhyankar, Local rings of high embedding dimension, Amer. J. Math. 89 (1967), 1073–1077. MR 220723, DOI 10.2307/2373418
- David J. Anick, A counterexample to a conjecture of Serre, Ann. of Math. (2) 115 (1982), no. 1, 1–33. MR 644015, DOI 10.2307/1971338
- Luchezar L. Avramov, Infinite free resolutions, Six lectures on commutative algebra (Bellaterra, 1996) Progr. Math., vol. 166, Birkhäuser, Basel, 1998, pp. 1–118. MR 1648664
- Rikard Bøgvad, Gorenstein rings with transcendental Poincaré-series, Math. Scand. 53 (1983), no. 1, 5–15. MR 733933, DOI 10.7146/math.scand.a-12010
- J. Elias and G. Valla, Structure theorems for certain Gorenstein ideals, Michigan J. of Math. 57 (2008), 269–292.
- J. Elias and G. Valla, Isomorphism classes of certain complete intersections, in preparation (2008).
- Tor H. Gulliksen and Gerson Levin, Homology of local rings, Queen’s Papers in Pure and Applied Mathematics, No. 20, Queen’s University, Kingston, Ont., 1969. MR 0262227
- Gerson L. Levin and Luchezar L. Avramov, Factoring out the socle of a Gorenstein ring, J. Algebra 55 (1978), no. 1, 74–83. MR 515760, DOI 10.1016/0021-8693(78)90191-6
- Maria Evelina Rossi and Giuseppe Valla, Stretched $\mathfrak {m}$-primary ideals, Beiträge Algebra Geom. 42 (2001), no. 1, 103–122. MR 1824753
- Judith D. Sally, The Poincaré series of stretched Cohen-Macaulay rings, Canadian J. Math. 32 (1980), no. 5, 1261–1265. MR 596109, DOI 10.4153/CJM-1980-094-0
- Judith D. Sally, Stretched Gorenstein rings, J. London Math. Soc. (2) 20 (1979), no. 1, 19–26. MR 545198, DOI 10.1112/jlms/s2-20.1.19
- Günter Scheja, Über die Bettizahlen lokaler Ringe, Math. Ann. 155 (1964), 155–172 (German). MR 162819, DOI 10.1007/BF01344078
Additional Information
- Juan Elias
- Affiliation: Departament d’Àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
- MR Author ID: 229646
- ORCID: 0000-0003-3053-1542
- Email: elias@ub.edu
- Giuseppe Valla
- Affiliation: Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy
- Email: valla@dima.unige.it
- Received by editor(s): March 31, 2008
- Published electronically: November 4, 2008
- Additional Notes: The first author was partially supported by MEC-FEDER MTM2007-67493
The second author was partially supported by MIUR - Communicated by: Bernd Ulrich
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 1175-1178
- MSC (2000): Primary 13D40; Secondary 13H10
- DOI: https://doi.org/10.1090/S0002-9939-08-09736-0
- MathSciNet review: 2465637