{"title":"解链手术，分支封面，椭圆表面上的铅笔","authors":"Terry Fuller","doi":"10.2140/agt.2023.23.2867","DOIUrl":null,"url":null,"abstract":"We show that every member of an infinite family of symplectic manifolds constructed by R. Inanc Baykur, Kenta Hayano, and Naoyuki Monden (arXiv:1903:02906) is diffeomorphic to an elliptic surface. As a result: (1) the symplectic Calabi-Yau 4-manifolds among their family are diffeomorphic to the standard K3 surface; (2) each elliptic surface E(n) admits a genus g Lefschetz pencil, for all g greater than or equal to n; and (3) each elliptic surface E(n) blown up once admits a pair of inequivalent genus g Lefschetz pencils, for all g greater than or equal to n.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"152 1","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Unchaining surgery, branched covers, and pencils on elliptic surfaces\",\"authors\":\"Terry Fuller\",\"doi\":\"10.2140/agt.2023.23.2867\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that every member of an infinite family of symplectic manifolds constructed by R. Inanc Baykur, Kenta Hayano, and Naoyuki Monden (arXiv:1903:02906) is diffeomorphic to an elliptic surface. As a result: (1) the symplectic Calabi-Yau 4-manifolds among their family are diffeomorphic to the standard K3 surface; (2) each elliptic surface E(n) admits a genus g Lefschetz pencil, for all g greater than or equal to n; and (3) each elliptic surface E(n) blown up once admits a pair of inequivalent genus g Lefschetz pencils, for all g greater than or equal to n.\",\"PeriodicalId\":50826,\"journal\":{\"name\":\"Algebraic and Geometric Topology\",\"volume\":\"152 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-09-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebraic and Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/agt.2023.23.2867\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebraic and Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/agt.2023.23.2867","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Unchaining surgery, branched covers, and pencils on elliptic surfaces
We show that every member of an infinite family of symplectic manifolds constructed by R. Inanc Baykur, Kenta Hayano, and Naoyuki Monden (arXiv:1903:02906) is diffeomorphic to an elliptic surface. As a result: (1) the symplectic Calabi-Yau 4-manifolds among their family are diffeomorphic to the standard K3 surface; (2) each elliptic surface E(n) admits a genus g Lefschetz pencil, for all g greater than or equal to n; and (3) each elliptic surface E(n) blown up once admits a pair of inequivalent genus g Lefschetz pencils, for all g greater than or equal to n.
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