Grothendieck-Serre formula and bigraded Cohen-Macaulay Rees algebras

Details Grothendieck-Serre formula and bigraded Cohen-Macaulay Rees algebras Grothendieck-Serre formula and bigraded Cohen-Macaulay Rees algebras

2002-06-19

arxiv.org/abs/math/0206192v1

Mathematics

Commutative Algebra

23 pages

Scientific paper

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.

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