Grothendieck-Serre formula and bigraded Cohen-Macaulay Rees algebras
Commutative Algebra
2007-05-23 v1
Abstract
The Grothendieck-Serre formula for the difference between the Hilbert function and Hilbert polynomial of a graded algebra is generalized for bigraded standard algebras. This is used to get a similar formula for the difference between the Bhattacharya function and Bhattacharya polynomial of two m-primary ideals I and J in a local ring (A,m) in terms of local cohomology modules of Rees algebras of I and J. The cohomology of a variation of the Kirby-Mehran complex for bigraded Rees algebras is studied which is used to characterize the Cohen-Macaulay property of bigraded Rees algebra of I and J for two dimensional Cohen-Macaulay local rings.
Keywords
Cite
@article{arxiv.math/0206192,
title = {Grothendieck-Serre formula and bigraded Cohen-Macaulay Rees algebras},
author = {A. V. Jayanthan and J. K. Verma},
journal= {arXiv preprint arXiv:math/0206192},
year = {2007}
}
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23 pages