|
On the Chern number of an ideal
Author(s):
Mousumi
Mandal;
J.
K.
Verma
Journal:
Proc. Amer. Math. Soc.
138
(2010),
1995-1999.
MSC (2010):
Primary 13D40, 13D07, 13H05
Posted:
February 4, 2010
MathSciNet review:
2596035
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
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:
-
- [1]
- W. Bruns and J. Herzog, Cohen-Macaulay Rings, Revised Edition, Cambridge University Press, Cambridge, 1998. MR 1251956 (95h:13020)
- [2]
- J. A. Eagon and D. G. Northcott, Ideals defined by matrices and a certain complex associated with them, Proc. Royal Soc. Ser. A 269 (1962), 188-204. MR 0142592 (26:161)
- [3]
- L. Ghezzi, J. Hong and W. Vasconcelos, The signature of the Chern coefficients of local rings, Math. Res. Lett. 16 (2009), 279-289. MR 2496744
- [4]
- S. Goto and K. Nishida, Hilbert coefficients and Buchsbaumness of associated graded rings, J. Pure Appl. Algebra 181 (2003), 61-74. MR 1971805 (2004k:13030)
- [5]
- V. Kodiyalam, Homological invariants of powers of an ideal, Proc. Amer. Math. Soc. 118 (1993), 757-764. MR 1156471 (93i:13022)
- [6]
- J-P. Serre, Local Algebra, Springer-Verlag, Berlin, 2000. MR 1771925 (2001b:13001)
- [7]
- W. Vasconcelos, The Chern coefficients of local rings, Michigan Math. J. 57 (2008), 725-743. MR 2492478 (2009m:13005)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2010):
13D40, 13D07, 13H05
Retrieve articles in all Journals with
MSC (2010):
13D40, 13D07, 13H05
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
Email:
jkv@math.iitb.ac.in
DOI:
10.1090/S0002-9939-10-10266-4
PII:
S 0002-9939(10)10266-4
Keywords:
Chern number,
Hilbert polynomial,
regular local ring
Received by editor(s):
February 24, 2009,
Received by editor(s) in revised form:
October 27, 2009
Posted:
February 4, 2010
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
