Nonsingular plane filling curves of minimum degree over a finite field and their automorphism groups: supplements to a work of Tallini
Nonsingular plane filling curves of minimum degree over a finite field and their automorphism groups: supplements to a work of Tallini
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有限域上最小次数的非奇异平面填充曲线及其自同构群：塔里尼作品的补充
DOI：
10.1016/j.laa.2012.08.032
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
S. J. Kim
中科院分区：
文献类型：
--
作者：
M. Homma;S. J. Kim
我们所关心的是定义在有限域F_q上的非奇异平面曲线，其中F_q包含射影平面的所有F_q-有理点。这种曲线的可能阶数至少为q+2。证明了具有该性质的q+2次非奇异平面曲线是存在的。更准确地说，我们明确地写下所有这些曲线。事实上，朱塞佩·塔林尼在1961年的旧论文中研究过这种曲线。我们解释了他的工作和我们的工作之间的联系。并从线性代数的观点，给出了他关于这类曲线的自同构群的结果的另一个证明。
Our concern is a nonsingular plane curve defined over a finite field Fqwhich includes all the Fq-rational points of the projective plane. The possible degree of such a curve is at least q+2. We prove that nonsingular plane curves of degree q+2 having the property actually exist. More precisely, we write down explicitly all of those curves. Actually, Giuseppe Tallini studied such curves in his old paper in 1961. We explain the connection between his work and ours. Also we give another proof of his result on the automorphism group of such a curve, from the viewpoint of linear algebra.