{"title":"论围堵I(3)∧I2和Böröczky线排列中三相点的构型","authors":"Jakub Kabat","doi":"10.12958/adm1959","DOIUrl":null,"url":null,"abstract":"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) ⊂ I2 is obtained when the number of lines is equal to 12.","PeriodicalId":364397,"journal":{"name":"Algebra and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the containment I(3) ⊂ I2 and configurationsof triple points in Böröczky line arrangements\",\"authors\":\"Jakub Kabat\",\"doi\":\"10.12958/adm1959\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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) ⊂ I2 is obtained when the number of lines is equal to 12.\",\"PeriodicalId\":364397,\"journal\":{\"name\":\"Algebra and Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra and Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12958/adm1959\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra and Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12958/adm1959","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the containment I(3) ⊂ I2 and configurationsof 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) ⊂ I2 is obtained when the number of lines is equal to 12.