{"title":"论平面克雷莫纳群中有限群的共轭问题","authors":"Ilya Karzhemanov","doi":"10.1016/j.jalgebra.2024.09.034","DOIUrl":null,"url":null,"abstract":"<div><div>We give a geometric condition for two finite subgroups <span><math><mi>G</mi><mo>≃</mo><msup><mrow><mi>G</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> of the plane Cremona group <span><math><msub><mrow><mi>Cr</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>C</mi><mo>)</mo></math></span> to be conjugate. The argument is based on the properties of a “Burnside-type” ring <span><math><mi>Ω</mi><mo>(</mo><msup><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mi>G</mi><mo>)</mo></math></span> encoding rational <em>G</em>-surfaces.</div></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the conjugacy problem for finite groups in the plane Cremona group\",\"authors\":\"Ilya Karzhemanov\",\"doi\":\"10.1016/j.jalgebra.2024.09.034\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We give a geometric condition for two finite subgroups <span><math><mi>G</mi><mo>≃</mo><msup><mrow><mi>G</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> of the plane Cremona group <span><math><msub><mrow><mi>Cr</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>C</mi><mo>)</mo></math></span> to be conjugate. The argument is based on the properties of a “Burnside-type” ring <span><math><mi>Ω</mi><mo>(</mo><msup><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mi>G</mi><mo>)</mo></math></span> encoding rational <em>G</em>-surfaces.</div></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-10-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021869324005490\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869324005490","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the conjugacy problem for finite groups in the plane Cremona group
We give a geometric condition for two finite subgroups of the plane Cremona group to be conjugate. The argument is based on the properties of a “Burnside-type” ring encoding rational G-surfaces.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
