Castelnuovo-Mumford regularity of Ext modules and homological degree
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- by Marc Chardin, Dao Thanh Ha and Lê Tuân Hoa PDF
- Trans. Amer. Math. Soc. 363 (2011), 3439-3456 Request permission
Abstract:
Bounds for the Castelnuovo-Mumford regularity of Ext modules, over a polynomial ring over a field, are given in terms of the initial degrees, Castelnuovo-Mumford regularities and the number of generators of the two graded modules involved. These general bounds are refined in the case where the second module is the ring. Other estimates, for instance on the size of graded pieces of these modules, are given. We also derive a bound on the homological degree in terms of the Castelnuovo-Mumford regularity. This answers positively a question raised by Vasconcelos.References
- Marc Chardin and Kamran Divaani-Aazar, Generalized local cohomology and regularity of Ext modules, J. Algebra 319 (2008), no. 11, 4780–4797. MR 2416743, DOI 10.1016/j.jalgebra.2007.11.032
- Marc Chardin, Amadou Lamine Fall, and Uwe Nagel, Bounds for the Castelnuovo-Mumford regularity of modules, Math. Z. 258 (2008), no. 1, 69–80. MR 2350034, DOI 10.1007/s00209-007-0157-9
- Luisa Rodrigues Doering, Tor Gunston, and Wolmer V. Vasconcelos, Cohomological degrees and Hilbert functions of graded modules, Amer. J. Math. 120 (1998), no. 3, 493–504. MR 1623400
- Dao Thanh Ha and Lê Tuân Hoa, Castelnuovo-Mumford regularity of some modules, Comm. Algebra 36 (2008), no. 3, 992–1004. MR 2394265, DOI 10.1080/00927870701776748
- Lê Tuân Hoa, Finiteness of Hilbert functions and bounds for Castelnuovo-Mumford regularity of initial ideals, Trans. Amer. Math. Soc. 360 (2008), no. 9, 4519–4540. MR 2403695, DOI 10.1090/S0002-9947-08-04424-3
- Lê Tuân Hoa and Eero Hyry, Castelnuovo-Mumford regularity of initial ideals, J. Symbolic Comput. 38 (2004), no. 5, 1327–1341. MR 2168718, DOI 10.1016/j.jsc.2004.04.001
- Lê Tuân Hoa and Eero Hyry, Castelnuovo-Mumford regularity of canonical and deficiency modules, J. Algebra 305 (2006), no. 2, 877–900. MR 2266858, DOI 10.1016/j.jalgebra.2006.05.001
- Uwe Nagel, Comparing Castelnuovo-Mumford regularity and extended degree: the borderline cases, Trans. Amer. Math. Soc. 357 (2005), no. 9, 3585–3603. MR 2146640, DOI 10.1090/S0002-9947-04-03595-0
- Peter Schenzel, Dualisierende Komplexe in der lokalen Algebra und Buchsbaum-Ringe, Lecture Notes in Mathematics, vol. 907, Springer-Verlag, Berlin-New York, 1982 (German). With an English summary. MR 654151
- Wolmer V. Vasconcelos, Computational methods in commutative algebra and algebraic geometry, Algorithms and Computation in Mathematics, vol. 2, Springer-Verlag, Berlin, 1998. With chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman. MR 1484973, DOI 10.1007/978-3-642-58951-5
Additional Information
- Marc Chardin
- Affiliation: Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 4, place Jussieu, F-75005 Paris, France
- MR Author ID: 259215
- Email: chardin@math.jussieu.fr
- Dao Thanh Ha
- Affiliation: Department of Mathematics, University of Vinh, Vietnam
- Email: thahanh@yahoo.com
- Lê Tuân Hoa
- Affiliation: Institute of Mathematics, 18 Hoang Quoc Viet Road, 10307 Hanoi, Vietnam
- Email: lthoa@math.ac.vn
- Received by editor(s): February 6, 2009
- Published electronically: February 8, 2011
- Additional Notes: The second and third authors were supported in part by the National Basic Research Program (Vietnam). The third author would also like to thank University of Paris 6 for their financial support and hospitality during his visit in 2007 when this work was started.
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 3439-3456
- MSC (2000): Primary 13D45
- DOI: https://doi.org/10.1090/S0002-9947-2011-05062-2
- MathSciNet review: 2775813