On the Number of Galois Points for a Plane Curve in Positive Characteristic

Abstract

We study Galois points for a plane smooth curve C ⊂ P ² of degree d ≥ 4 in characteristic p > 2. We generalize Yoshihara's result on the number of inner (resp., outer) Galois points to positive characteristic under the assumption that d ≢ 1 (resp., d ≢ 0) modulo p. As an application, we also find the number of Galois points in the case that d = p.

Key Words:

• Galois point
• Plane curve
• Positive characteristic

2000 Mathematics Subject Classification:

• 12F10
• 14H05
• 14H50

ACKNOWLEDGMENT

The author is grateful to Professor Hisao Yoshihara for helpful advice. The author thanks Professor Kei Miura for valuable discussions. The author also thanks the referee for careful reading and thoughtful comments. Especially, the short summary on Wronskian divisors in Section 2 is based on the referee's comments.

Notes

Communicated by S. Kleiman.