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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 2022, Vol.216 (1), Article 8 |
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Main Authors: | , , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | 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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ISSN: | 0046-5755 1572-9168 |
DOI: | 10.1007/s10711-021-00672-5 |