Superspecial curves of genus 4 in small characteristic
Superspecial curves of genus 4 in small characteristic
复制标题
小特征4属超特殊曲线
DOI：
10.1016/j.ffa.2016.12.001
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发表时间：
2017
影响因子：
1
通讯作者：
Momonari Kudo and Shushi Harashita
中科院分区：
文献类型：
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作者：
H. Ki;Y. Komori and M. Suzuki;Masatoshi Suzuki;Masatoshi Suzuki;Masatoshi Suzuki;Masatoshi Suzuki;Masatoshi Suzuki;Momonari Kudo and Shushi Harashita
本文对特征p≤7中亏格4的超特殊曲线进行了完整的研究，证明了特征7中不存在亏格4的超特殊曲线，这是对Ekedahl[9]于1987年提出的亏格4问题的否定回答.这意味着在F49上不存在亏格4的极大曲线，这在许多点上更新了表。Org.给出了任意p≥5中超特殊非超椭圆曲线的计数算法，并在计算机代数系统MAGMA上实现了它对p≤7的计数.我们在p=5中的结果再次证明了F25上亏格4的极大曲线的唯一性，原始的理论证明见[11]。在附录中，我们给出了确定完全交曲线的Hasse-Witt矩阵的一般方法。
This paper contains a complete study of superspecial curves of genus 4 in characteristic p≤ 7. We prove that there does not exist a superspecial curve of genus 4 in characteristic 7. This is a negative answer to the genus 4 case of the problem proposed by Ekedahl [9] in 1987. This implies the non-existence of maximal curve of genus 4 over F 49, which updates the table at manypoints. org. We give an algorithm to enumerate superspecial nonhyperelliptic curves in arbitrary p≥ 5, and for p≤ 7 we execute it with our implementation on a computer algebra system Magma. Our result in p= 5 re-proves the uniqueness of maximal curves of genus 4 over F 25, see [11] for the original theoretical proof. In Appendix, we present a general method determining Hasse–Witt matrices of curves which are complete intersections.