Abstract
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.
The first author is partially supported by a grant from Infosys Foundation; The second author is supported by CSIR Fellowship of Government of India.
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We thank Professor Markus Brodmann for discussions.
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Masuti, S.K., Sarkar, P., Verma, J.K. (2016). Variations on the Grothendieck–Serre Formula for Hilbert Functions and Their Applications. In: Rizvi, S., Ali, A., Filippis, V. (eds) Algebra and its Applications. Springer Proceedings in Mathematics & Statistics, vol 174. Springer, Singapore. https://doi.org/10.1007/978-981-10-1651-6_8
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