On the existence of superspecial and maximal nonhyperelliptic curves of genera four and five
On the existence of superspecial and maximal nonhyperelliptic curves of genera four and five
复制标题
论四属和五属超特殊极大非超椭圆曲线的存在性
DOI：
10.1080/00927872.2019.1609013
复制
发表时间：
2019
影响因子：
0.7
通讯作者：
Kudo Momonari
中科院分区：
文献类型：
--
作者：
Kudo Momonari;Harashita Shushi;Kudo Momonari
本文证明了对于无穷多个素数sp，特征p> 0的属四和属五的超特殊和最大非超椭圆曲线的存在性。具体来说，我们证明p> 2的射影三空间中的簇是属四的最大超特殊非超椭圆曲线当且仅当我们还证明去奇异化Tpo是属五的最大超特殊三角曲线当且仅当且此外，我们给出了更一般类型的最大曲线族，其中包括Tp。
This article shows the existence of superspecial and maximal nonhyperelliptic curves of genera four and five in characteristicp> 0 for infinitely many primesp. Specifically, we prove that the varietyin the projective three-space withp> 2 is a maximal superspecial nonhyperelliptic curve of genus four if and only ifWe also prove that the desingularizationTpofis a maximal superspecial trigonal curve of genus five if and only iforMoreover, we give families of maximal curves of more general type, which includeTp.