Evaluations of initial ideals and Castelnuovo-Mumford regularity
HTML articles powered by AMS MathViewer
- by Ngô Viêt Trung
- Proc. Amer. Math. Soc. 130 (2002), 1265-1274
- DOI: https://doi.org/10.1090/S0002-9939-01-06216-5
- Published electronically: October 5, 2001
- PDF | Request permission
Abstract:
This paper characterizes the Castelnuovo-Mumford regularity by evaluating the initial ideal with respect to the reverse lexicographic order.References
- A. Aramova and J. Herzog, Almost regular sequences and Betti numbers, Amer. J. Math. 122 (2000), no. 4, 689–719.
- Dave Bayer, Hara Charalambous, and Sorin Popescu, Extremal Betti numbers and applications to monomial ideals, J. Algebra 221 (1999), no. 2, 497–512. MR 1726711, DOI 10.1006/jabr.1999.7970
- Dave Bayer and David Mumford, What can be computed in algebraic geometry?, Computational algebraic geometry and commutative algebra (Cortona, 1991) Sympos. Math., XXXIV, Cambridge Univ. Press, Cambridge, 1993, pp. 1–48. MR 1253986
- David Bayer and Michael Stillman, A criterion for detecting $m$-regularity, Invent. Math. 87 (1987), no. 1, 1–11. MR 862710, DOI 10.1007/BF01389151
- Isabel Bermejo and Philippe Gimenez, On Castelnuovo-Mumford regularity of projective curves, Proc. Amer. Math. Soc. 128 (2000), no. 5, 1293–1299. MR 1646319, DOI 10.1090/S0002-9939-99-05184-9
- Winfried Bruns and Jürgen Herzog, On multigraded resolutions, Math. Proc. Cambridge Philos. Soc. 118 (1995), no. 2, 245–257. MR 1341789, DOI 10.1017/S030500410007362X
- Laurence Coudurier and Marcel Morales, Classification des courbes toriques dans l’espace projectif, module de Rao et liaison, J. Algebra 211 (1999), no. 2, 524–548 (French). MR 1666657, DOI 10.1006/jabr.1998.7739
- 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
- L.T. Hoa and N.V. Trung, On the Castelnuovo-Mumford regularity and the arithmetic degree of monomial ideals, Math. Z. 229 (1998), 519-537.
- Sam Perlis, Maximal orders in rational cyclic algebras of composite degree, Trans. Amer. Math. Soc. 46 (1939), 82–96. MR 15, DOI 10.1090/S0002-9947-1939-0000015-X
- Peter Schenzel, Ngô Viêt Trung, and Nguyễn Tụ’ Cu’ò’ng, Verallgemeinerte Cohen-Macaulay-Moduln, Math. Nachr. 85 (1978), 57–73 (German). MR 517641, DOI 10.1002/mana.19780850106
- N.V. Trung, Reduction exponent and degree bounds for the defining equations of a graded ring, Proc. Amer. Math. Soc. 102 (1987), 229-236.
- Ngô Viêt Trung, Gröbner bases, local cohomology and reduction number, Proc. Amer. Math. Soc. 129 (2001), no. 1, 9–18. MR 1695103, DOI 10.1090/S0002-9939-00-05503-9
- Wolmer V. Vasconcelos, Cohomological degrees of graded modules, Six lectures on commutative algebra (Bellaterra, 1996) Progr. Math., vol. 166, Birkhäuser, Basel, 1998, pp. 345–392. MR 1648669
Bibliographic Information
- Ngô Viêt Trung
- Affiliation: Institute of Mathematics, Box 631, Bò Hô, Hanoi, Vietnam
- MR Author ID: 207806
- Email: nvtrung@hn.vnn.vn
- Received by editor(s): May 19, 2000
- Received by editor(s) in revised form: October 29, 2000
- Published electronically: October 5, 2001
- Additional Notes: The author was partially supported by the National Basic Research Program of Vietnam.
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1265-1274
- MSC (1991): Primary 13D02, 13P10
- DOI: https://doi.org/10.1090/S0002-9939-01-06216-5
- MathSciNet review: 1879946