Trisections on certain rational elliptic surfaces and families of Zariski pairs degenerating to the same conic-line arrangement
In this paper, we study the geometry of trisections of certain rational elliptic surfaces. We utilize Mumford representations of semi-reduced divisors in our study and demonstrate its effectiveness in dealing with equations of trisections and related plane curves. As an application, we construct pla...
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| Published in: | Geometriae dedicata Vol. 216; no. 1 |
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| Language: | English |
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| Abstract | In this paper, we study the geometry of trisections of certain rational elliptic surfaces. We utilize Mumford representations of semi-reduced divisors in our study and demonstrate its effectiveness in dealing with equations of trisections and related plane curves. As an application, we construct plane curves with interesting properties. Especially, we give explicit equations of plane curves which give a family of Zariski pairs consisting of cubic-conic-line arrangements that degenerate to the same conic-line arrangement. |
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| AbstractList | In this paper, we study the geometry of trisections of certain rational elliptic surfaces. We utilize Mumford representations of semi-reduced divisors in our study and demonstrate its effectiveness in dealing with equations of trisections and related plane curves. As an application, we construct plane curves with interesting properties. Especially, we give explicit equations of plane curves which give a family of Zariski pairs consisting of cubic-conic-line arrangements that degenerate to the same conic-line arrangement. |
| ArticleNumber | 8 |
| Author | Bannai, S. Kawana, N. Masuya, R. Tokunaga, H. |
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| Keywords | Mordell-Weil lattice Elliptic surfaces 14J27 13P10 14Q05 Multisections Topology of reducible plane curves 14D06 |
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| References | Shioda (CR21) 1990; 39 Bannai, Tokunaga, Yamamoto (CR8) 2020; 49 CR18 Silverman (CR22) 2009 CR16 CR14 CR12 Kodaira (CR13) 1963; 77 Menezes, Wu, Zuccherato, Koblitz (CR15) 1998 Bannai, Tokunaga (CR7) 2021; 221 Tokunaga (CR25) 2012; 35 Bannai, Tokunaga (CR5) 2017; 231 Bannai, Tokunaga (CR6) 2020; 96 CR2 Miranda, Persson (CR17) 1986; 193 Oguiso, Shioda (CR19) 1991; 40 Bannai, Tokunaga (CR4) 2015; 178 CR9 Horikawa (CR11) 1975; 31 CR24 Artal Bartolo (CR1) 1994; 3 Galbraith (CR10) 2012 CR23 CR20 Tokunaga (CR26) 2014; 66 Bannai (CR3) 2016; 202 E Horikawa (672_CR11) 1975; 31 S Bannai (672_CR5) 2017; 231 K Oguiso (672_CR19) 1991; 40 R Miranda (672_CR17) 1986; 193 JH Silverman (672_CR22) 2009 S Bannai (672_CR4) 2015; 178 S Bannai (672_CR6) 2020; 96 T Shioda (672_CR21) 1990; 39 S Bannai (672_CR8) 2020; 49 672_CR12 H Tokunaga (672_CR25) 2012; 35 672_CR16 S Bannai (672_CR3) 2016; 202 672_CR2 672_CR14 S Bannai (672_CR7) 2021; 221 H Tokunaga (672_CR26) 2014; 66 K Kodaira (672_CR13) 1963; 77 672_CR18 AJ Menezes (672_CR15) 1998 672_CR9 E Artal Bartolo (672_CR1) 1994; 3 SD Galbraith (672_CR10) 2012 672_CR20 672_CR23 672_CR24 |
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| SubjectTerms | Algebraic Geometry Convex and Discrete Geometry Curves Differential Geometry Hyperbolic Geometry Mathematical analysis Mathematics Mathematics and Statistics Original Paper Projective Geometry Topology |
| Title | Trisections on certain rational elliptic surfaces and families of Zariski pairs degenerating to the same conic-line arrangement |
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