On the Chern number of an ideal
HTML articles powered by AMS MathViewer
- by Mousumi Mandal and J. K. Verma PDF
- Proc. Amer. Math. Soc. 138 (2010), 1995-1999 Request permission
Abstract:
We settle the negativity conjecture of Vasconcelos for the Chern number of an ideal in certain unmixed quotients of regular local rings by explicit calculation of the Hilbert polynomials of all ideals generated by a system of parameters.References
- Winfried Bruns and Jürgen Herzog, Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, vol. 39, Cambridge University Press, Cambridge, 1993. MR 1251956
- J. A. Eagon and D. G. Northcott, Ideals defined by matrices and a certain complex associated with them, Proc. Roy. Soc. London Ser. A 269 (1962), 188–204. MR 142592, DOI 10.1098/rspa.1962.0170
- Laura Ghezzi, Jooyoun Hong, and Wolmer V. Vasconcelos, The signature of the Chern coefficients of local rings, Math. Res. Lett. 16 (2009), no. 2, 279–289. MR 2496744, DOI 10.4310/MRL.2009.v16.n2.a6
- Shiro Goto and Koji Nishida, Hilbert coefficients and Buchsbaumness of associated graded rings, J. Pure Appl. Algebra 181 (2003), no. 1, 61–74. MR 1971805, DOI 10.1016/S0022-4049(02)00325-0
- Vijay Kodiyalam, Homological invariants of powers of an ideal, Proc. Amer. Math. Soc. 118 (1993), no. 3, 757–764. MR 1156471, DOI 10.1090/S0002-9939-1993-1156471-5
- Jean-Pierre Serre, Local algebra, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2000. Translated from the French by CheeWhye Chin and revised by the author. MR 1771925, DOI 10.1007/978-3-662-04203-8
- Wolmer V. Vasconcelos, The Chern coefficients of local rings, Michigan Math. J. 57 (2008), 725–743. Special volume in honor of Melvin Hochster. MR 2492478, DOI 10.1307/mmj/1220879434
Additional Information
- Mousumi Mandal
- Affiliation: Department of Mathematics, India Institute of Technology Bombay, Mumbai 400 076, India
- Email: mousumi@math.iitb.ac.in
- J. K. Verma
- Affiliation: Department of Mathematics, India Institute of Technology Bombay, Mumbai 400 076, India
- MR Author ID: 177990
- Email: jkv@math.iitb.ac.in
- Received by editor(s): February 24, 2009
- Received by editor(s) in revised form: October 27, 2009
- Published electronically: February 4, 2010
- Communicated by: Bernd Ulrich
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1995-1999
- MSC (2010): Primary 13D40, 13D07, 13H05
- DOI: https://doi.org/10.1090/S0002-9939-10-10266-4
- MathSciNet review: 2596035