Variations on the Grothendieck-Serre Formula for Hilbert functions and   their applications
  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. 
Shreedevi K. Masuti, Parangama Sarkar and J. K. Verma
math.AC