## On the structure of the Sally module and the second normal Hilbert coefficient

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- by Shreedevi K. Masuti, Kazuho Ozeki, Maria Evelina Rossi and Hoang Le Truong PDF
- Proc. Amer. Math. Soc.
**148**(2020), 2757-2771 Request permission

## Abstract:

The Hilbert coefficients of the normal filtration give important geometric information on the base ring like the pseudo-rationality. The Sally module was introduced by W.V. Vasconcelos and it is useful to connect the Hilbert coefficients to the homological properties of the associated graded module of a Noetherian filtration. In this paper we give a complete structure of the Sally module in the case the second normal Hilbert coefficient attains almost minimal value in an analytically unramified Cohen-Macaulay local ring. As a consequence, in this case we present a complete description of the Hilbert function of the associated graded ring of the normal filtration. A deep analysis of the vanishing of the third normal Hilbert coefficient has been necessary. This study is related to a longstanding conjecture stated by S. Itoh.## References

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## Additional Information

**Shreedevi K. Masuti**- Affiliation: IIT Dharwad, WALMI Campus, PB Road, near High Court, Dharwad - 580011, Karnataka, India
- MR Author ID: 1035451
- Email: shreedevi@iitdh.ac.in
**Kazuho Ozeki**- Affiliation: Department of Mathematical Sciences, Faculty of Science, Yamaguchi University, 1677-1 Yoshida, Yamaguchi 753-8512, Japan
- MR Author ID: 850709
- Email: ozeki@yamaguchi-u.ac.jp
**Maria Evelina Rossi**- Affiliation: Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy
- MR Author ID: 150830
- ORCID: 0000-0001-7039-5296
- Email: rossim@dima.unige.it
**Hoang Le Truong**- Affiliation: Mathematik und Informatik, Universität des Saarlandes, Campus E2 4, D-66123 Saarbrücken, Germany; Institute of Mathematics, VAST, 18 Hoang Quoc Viet Road, 10307, Hanoi, Viet Nam; and Thang Long Institute of Mathematics and Applied Sciences, Hanoi, Vietnam
- MR Author ID: 842253
- Email: hoang@math.uni-sb.de, hltruong@math.ac.vn, truonghoangle@gmail.com
- Received by editor(s): March 7, 2019
- Published electronically: April 14, 2020
- Additional Notes: The first author was supported by the INSPIRE faculty award funded by the Department of Science and Technology, Govt. of India. She was also partially supported by a grant from the Infosys Foundation. She was supported by the INdAM COFUND Fellowships cofunded by Marie Curie actions, Italy, for her research in Genova during which this work was started

The second author was partially supported by Grant-in-Aid for Scientific Researches (C) in Japan (18K03241)

The third author was partially supported by PRIN 2015EYPTSB-008 Geometry of Algebraic Varieties

The fourth author was partially supported by the Alexander von Humboldt Foundation and the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.04-2019.309 - Communicated by: Claudia Polini
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**148**(2020), 2757-2771 - MSC (2010): Primary 13D40, 13A30, 13H10
- DOI: https://doi.org/10.1090/proc/14839
- MathSciNet review: 4099766