Variations on the Grothendieck–Serre Formula for Hilbert Functions and Their Applications

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 174)


In this expository paper, we present proofs of Grothendieck–Serre formula for multi-graded algebras and Rees algebras for admissible multi-graded filtrations. As applications, we derive formulas of Sally for postulation number of admissible filtrations and Hilbert coefficients. We also discuss a partial solution of Itoh’s conjecture by Kummini and Masuti. We present an alternate proof of Huneke–Ooishi Theorem and a generalisation for multi-graded filtrations.


Hilbert polynomial Admissible filtration Normal Hilbert polynomial Joint reduction Local cohomology Rees algebra Multi-graded filtration Grothendieck–Serre formula 



We thank Professor Markus Brodmann for discussions.


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© Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Chennai Mathematical InstituteChennaiIndia
  2. 2.Department of MathematicsIndian Institute of Technology BombayMumbaiIndia

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