Buchsbaum Stanley–Reisner rings with minimal multiplicity
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- by Naoki Terai and Ken-ichi Yoshida
- Proc. Amer. Math. Soc. 134 (2006), 55-65
- DOI: https://doi.org/10.1090/S0002-9939-05-08176-1
- Published electronically: August 15, 2005
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Abstract:
In this paper, we study Buchsbaum Stanley–Reisner rings with linear free resolution. We introduce the notion of Buchsbaum Stanley–Reisner rings with minimal multiplicity of initial degree $q$, which extends the notion of Buchsbaum rings with minimal multiplicity defined by Goto. As an application, we give many examples of non-Cohen–Macaulay Buchsbaum Stanley–Reisner rings with linear resolution.References
- Winfried Bruns and Jürgen Herzog, Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, vol. 39, Cambridge University Press, Cambridge, 1993. MR 1251956
- Winfried Bruns and Takayuki Hibi, Stanley-Reisner rings with pure resolutions, Comm. Algebra 23 (1995), no. 4, 1201–1217. MR 1317395, DOI 10.1080/00927879508825274
- John A. Eagon and Victor Reiner, Resolutions of Stanley-Reisner rings and Alexander duality, J. Pure Appl. Algebra 130 (1998), no. 3, 265–275. MR 1633767, DOI 10.1016/S0022-4049(97)00097-2
- David Eisenbud and Shiro Goto, Linear free resolutions and minimal multiplicity, J. Algebra 88 (1984), no. 1, 89–133. MR 741934, DOI 10.1016/0021-8693(84)90092-9
- Ralf Fröberg, Rings with monomial relations having linear resolutions, J. Pure Appl. Algebra 38 (1985), no. 2-3, 235–241. MR 814179, DOI 10.1016/0022-4049(85)90011-8
- Ralf Fröberg, On Stanley-Reisner rings, Topics in algebra, Part 2 (Warsaw, 1988) Banach Center Publ., vol. 26, PWN, Warsaw, 1990, pp. 57–70. MR 1171260
- Shiro Goto, Buchsbaum rings of maximal embedding dimension, J. Algebra 76 (1982), no. 2, 383–399. MR 661862, DOI 10.1016/0021-8693(82)90221-6
- Shiro Goto, On the associated graded rings of parameter ideals in Buchsbaum rings, J. Algebra 85 (1983), no. 2, 490–534. MR 725097, DOI 10.1016/0021-8693(83)90109-6
- J. Herzog and M. Kühl, On the Betti numbers of finite pure and linear resolutions, Comm. Algebra 12 (1984), no. 13-14, 1627–1646. MR 743307, DOI 10.1080/00927878408823070
- Takayuki Hibi, Buchsbaum complexes with linear resolutions, J. Algebra 179 (1996), no. 1, 127–136. MR 1367844, DOI 10.1006/jabr.1996.0006
- Lê Tuân Hoa and Chikashi Miyazaki, Bounds on Castelnuovo-Mumford regularity for generalized Cohen-Macaulay graded rings, Math. Ann. 301 (1995), no. 3, 587–598. MR 1324528, DOI 10.1007/BF01446647
- Peter Schenzel, Über die freien Auflösungen extremaler Cohen-Macaulay-Ringe, J. Algebra 64 (1980), no. 1, 93–101 (German). MR 575785, DOI 10.1016/0021-8693(80)90136-2
- Richard P. Stanley, Combinatorics and commutative algebra, 2nd ed., Progress in Mathematics, vol. 41, Birkhäuser Boston, Inc., Boston, MA, 1996. MR 1453579
- Jürgen Stückrad and Wolfgang Vogel, Buchsbaum rings and applications, Springer-Verlag, Berlin, 1986. An interaction between algebra, geometry and topology. MR 881220, DOI 10.1007/978-3-662-02500-0
- Naoki Terai, On $h$-vectors of Buchsbaum Stanley-Reisner rings, Hokkaido Math. J. 25 (1996), no. 1, 137–148. MR 1376497, DOI 10.14492/hokmj/1351516714
- Naoki Terai, Alexander duality theorem and Stanley-Reisner rings, Sūrikaisekikenkyūsho K\B{o}kyūroku 1078 (1999), 174–184. Free resolutions of coordinate rings of projective varieties and related topics (Japanese) (Kyoto, 1998). MR 1715588
- Naoki Terai, Eisenbud-Goto inequality for Stanley-Reisner rings, Geometric and combinatorial aspects of commutative algebra (Messina, 1999) Lecture Notes in Pure and Appl. Math., vol. 217, Dekker, New York, 2001, pp. 379–391. MR 1824243
- N. Terai and T. Hibi, Computation of Betti numbers of monomial ideals associated with cyclic polytopes, Discrete Comput. Geom. 15 (1996), no. 3, 287–295. MR 1380395, DOI 10.1007/BF02711496
Bibliographic Information
- Naoki Terai
- Affiliation: Department of Mathematics, Faculty of Culture and Education, Saga University, Saga 840–8502, Japan
- Email: terai@cc.saga-u.ac.jp
- Ken-ichi Yoshida
- Affiliation: Graduate School of Mathematics, Nagoya University, Nagoya 464–8602, Japan
- MR Author ID: 359418
- Email: yoshida@math.nagoya-u.ac.jp
- Received by editor(s): August 28, 2004
- Published electronically: August 15, 2005
- Communicated by: Bernd Ulrich
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 55-65
- MSC (2000): Primary 13F55; Secondary 13D02
- DOI: https://doi.org/10.1090/S0002-9939-05-08176-1
- MathSciNet review: 2170543