A sharp bound for the resurgence of sums of ideals
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- by Do Van Kien, Hop D. Nguyen and Le Minh Thuan
- Proc. Amer. Math. Soc. 152 (2024), 1405-1418
- DOI: https://doi.org/10.1090/proc/16655
- Published electronically: January 26, 2024
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Abstract:
We prove a sharp upper bound for the resurgence of sums of ideals involving disjoint sets of variables, strengthening work of Bisui–Hà–Jayanthan–Thomas [Collect. Math. 72 (2021), pp. 605–614]. Complete solutions are delivered for two conjectures proposed by these authors. For given real numbers $a$ and $b$, we consider the set $Res(a,b)$ of possible values of the resurgence of $I+J$ where $I$ and $J$ are ideals in disjoint sets of variables having resurgence $a$ and $b$, respectively. Some questions and partial results about $Res(a,b)$ are discussed.References
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Bibliographic Information
- Do Van Kien
- Affiliation: Department of Mathematics, Hanoi Pedagogical University 2, Vinh Phuc, Viet Nam
- MR Author ID: 1272869
- Email: dovankien@hpu2.edu.vn
- Hop D. Nguyen
- Affiliation: Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam
- MR Author ID: 981901
- Email: ngdhop@gmail.com
- Le Minh Thuan
- Affiliation: Department of Mathematics, Hanoi Pedagogical University 2, Vinh Phuc, Viet Nam
- Email: leminhthuan1998cp@gmail.com
- Received by editor(s): October 27, 2022
- Received by editor(s) in revised form: July 14, 2023
- Published electronically: January 26, 2024
- Additional Notes: This work was partially supported by a grant from the International Centre for Research and Postgraduate Training in Mathematics, VAST (grant number ICRTM03_2020.05). The first author was funded by the Foundation for Science and Technology Development, Hanoi Pedagogical University 2 via grant number HPU2.2023-UT-09. The second author was supported from the Simons Foundation Targeted Grant for the Institute of Mathematics - VAST (Award number: 558672), and from the Vietnam Academy of Science and Technology (grants CSCL01.01/22-23 and NCXS02.01/22-23).
- Communicated by: Claudia Polini
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 1405-1418
- MSC (2020): Primary 13F20, 14N05, 13A02
- DOI: https://doi.org/10.1090/proc/16655
- MathSciNet review: 4709214