Quasi-Galois points, II: Arrangements
Satoru Fukasawa, Kei Miura, Takeshi Takahashi
TL;DR
This paper studies the distribution and properties of quasi-Galois points on smooth plane curves, especially focusing on quartic and sextic curves with many such points, advancing understanding of their automorphism groups.
Contribution
It characterizes smooth plane curves with many quasi-Galois points, particularly quartic and sextic curves, building on the foundational concept introduced in Part I.
Findings
Quartic curves with many quasi-Galois points are characterized.
Sextic curves with many quasi-Galois points are characterized.
The number of quasi-Galois points on smooth plane curves is described.
Abstract
In Part I, the present authors introduced the notion of a quasi-Galois point, for investigating the automorphism groups of plane curves. In this second part, the number of quasi-Galois points for smooth plane curves is described. In particular, sextic or quartic curves with many quasi-Galois points are characterized.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Numerical Analysis Techniques · Vietnamese History and Culture Studies