On the Number of Galois Points for a Plane Curve in Positive Characteristic
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Abstract
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 pointPlane curvePositive characteristic2000 Mathematics Subject Classification: 12F1014H0514H50 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.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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