## The reduction number and degree bound of projective subschemes

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- by Đoàn Trung Cường and Sijong Kwak PDF
- Trans. Amer. Math. Soc.
**373**(2020), 1153-1180 Request permission

## Abstract:

In this paper, we prove the degree upper bound of projective subschemes in terms of the reduction number and show that the maximal cases are only arithmetically Cohen–Macaulay with linear resolutions. Furthermore, it can be shown that there are only two types of reduced, irreducible projective varieties with almost maximal degree. We also give the possible explicit Betti tables for almost maximal cases. In addition, interesting examples are provided to understand our main results.## References

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## Additional Information

**Đoàn Trung Cường**- Affiliation: Institute of Mathematics and the Graduate University of Science and Technology, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam
- Email: dtcuong@math.ac.vn
**Sijong Kwak**- Affiliation: Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, 373-1 Gusung-dong, Yusung-Gu, Daejeon, Republic of Korea
- MR Author ID: 633321
- Email: sjkwak@kaist.ac.kr
- Received by editor(s): December 16, 2018
- Received by editor(s) in revised form: June 22, 2019
- Published electronically: November 5, 2019
- Additional Notes: The first author was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.04-2015.26. This work was done during his visit to the Korea Advanced Institute of Science and Technology (KAIST). He thanks Professor Sijong Kwak and KAIST for their support and hospitality during his visit.

The second author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Science and ICT (2015R1A2A2A01004545). - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**373**(2020), 1153-1180 - MSC (2010): Primary 14N05; Secondary 13D02
- DOI: https://doi.org/10.1090/tran/7965
- MathSciNet review: 4068260