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Transactions of the American Mathematical Society

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The reduction number and degree bound of projective subschemes

Authors: Đoàn Trung Cường and Sijong Kwak
Journal: Trans. Amer. Math. Soc. 373 (2020), 1153-1180
MSC (2010): Primary 14N05; Secondary 13D02
Published electronically: November 5, 2019
MathSciNet review: 4068260
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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.

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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

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

Keywords: Reduction number, degree, Castelnuovo–Mumford regularity, arithmetically Cohen–Macaulay subscheme, Betti table
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).
Article copyright: © Copyright 2019 American Mathematical Society