On the containment \(I^{(3)} \subset I^{2}\) and configurations of triple points in Böröczky line arrangements
We study sets of triple points of Böröczky's arrangements of lines in the context of the containment problem proposed by Harbourne and Huneke. We show that in the class of those arrangements, the smallest counterexample to the containment \(I^{(3)} \subset I^{2}\) is obtained when the number of...
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| Видавець: | Lugansk National Taras Shevchenko University |
|---|---|
| Дата: | 2023 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2023
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1959 |
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Algebra and Discrete Mathematics| id |
oai:ojs.admjournal.luguniv.edu.ua:article-1959 |
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oai:ojs.admjournal.luguniv.edu.ua:article-19592023-10-30T03:20:23Z On the containment \(I^{(3)} \subset I^{2}\) and configurations of triple points in Böröczky line arrangements Kabat, J. ideals, line arrangements, containment problem, Harbourne--Huneke problem 14C20, 13C05, 52C35 We study sets of triple points of Böröczky's arrangements of lines in the context of the containment problem proposed by Harbourne and Huneke. We show that in the class of those arrangements, the smallest counterexample to the containment \(I^{(3)} \subset I^{2}\) is obtained when the number of lines is equal to \(12\). Lugansk National Taras Shevchenko University Jakub Kabat was partially supported by the National Science Center (Poland) Preludium Grant Nr UMO 2018/31/N/ST1/02101 2023-10-12 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1959 10.12958/adm1959 Algebra and Discrete Mathematics; Vol 35, No 2 (2023) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1959/pdf Copyright (c) 2023 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
ideals line arrangements containment problem Harbourne--Huneke problem 14C20 13C05 52C35 |
| spellingShingle |
ideals line arrangements containment problem Harbourne--Huneke problem 14C20 13C05 52C35 Kabat, J. On the containment \(I^{(3)} \subset I^{2}\) and configurations of triple points in Böröczky line arrangements |
| topic_facet |
ideals line arrangements containment problem Harbourne--Huneke problem 14C20 13C05 52C35 |
| format |
Article |
| author |
Kabat, J. |
| author_facet |
Kabat, J. |
| author_sort |
Kabat, J. |
| title |
On the containment \(I^{(3)} \subset I^{2}\) and configurations of triple points in Böröczky line arrangements |
| title_short |
On the containment \(I^{(3)} \subset I^{2}\) and configurations of triple points in Böröczky line arrangements |
| title_full |
On the containment \(I^{(3)} \subset I^{2}\) and configurations of triple points in Böröczky line arrangements |
| title_fullStr |
On the containment \(I^{(3)} \subset I^{2}\) and configurations of triple points in Böröczky line arrangements |
| title_full_unstemmed |
On the containment \(I^{(3)} \subset I^{2}\) and configurations of triple points in Böröczky line arrangements |
| title_sort |
on the containment \(i^{(3)} \subset i^{2}\) and configurations of triple points in böröczky line arrangements |
| description |
We study sets of triple points of Böröczky's arrangements of lines in the context of the containment problem proposed by Harbourne and Huneke. We show that in the class of those arrangements, the smallest counterexample to the containment \(I^{(3)} \subset I^{2}\) is obtained when the number of lines is equal to \(12\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2023 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1959 |
| work_keys_str_mv |
AT kabatj onthecontainmenti3subseti2andconfigurationsoftriplepointsinboumlroumlczkylinearrangements |
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2024-04-12T06:13:53Z |
| last_indexed |
2024-04-12T06:13:53Z |
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1804810505633660928 |