2020年
Torsion divisors of plane curves with maximal flexes and Zariski pairs
Mathematische Nachrichten, to appear.
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- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
There is a close relationship between the embedded topology of complex plane
curves and the arithmetics of elliptic curves. In a recent paper, we studied
the topology of some arrangements of curves which include a special smooth
component, via the torsion properties induced by the divisors in the special
curve associated to the rest of the components, which is an arithmetic
property. When this special curve has maximal flexes, there is a natural
isomorphism between its Jacobian variety and the degree zero part of its Picard
group. In this paper we consider curve arrangements which contain a special
smooth component with a maximal flex and exploit these properties to obtain
Zariski tuples which show the interplay between topology, geometry and
arithmetics.
curves and the arithmetics of elliptic curves. In a recent paper, we studied
the topology of some arrangements of curves which include a special smooth
component, via the torsion properties induced by the divisors in the special
curve associated to the rest of the components, which is an arithmetic
property. When this special curve has maximal flexes, there is a natural
isomorphism between its Jacobian variety and the degree zero part of its Picard
group. In this paper we consider curve arrangements which contain a special
smooth component with a maximal flex and exploit these properties to obtain
Zariski tuples which show the interplay between topology, geometry and
arithmetics.
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- ID情報
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- arXiv ID : arXiv:2005.12673