Grothendieck–Serre formula and bigraded Cohen–Macaulay Rees algebras

✍ Scribed by A.V. Jayanthan; J.K. Verma

• Book ID: 104140356
• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 172 KB
• Volume: 254
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(02)00101-1

✦ Synopsis

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.