2021 年 73 巻 2 号 p. 505-524
For a relatively minimal fibration 𝑓 : 𝑋 → ℙ1 of non-hyperelliptic curves of genus 𝑔, we know the Picard number 𝜌(𝑋) ≤ 3𝑔 + 8. We study the case where 𝜌(𝑋) = 3𝑔 + 8 and the Mordell–Weil group of 𝑓 is trivial. Such an 𝑓 occurs only if 𝑔 ≡ 0 or 1 (mod 3), and we describe such 𝑓 : 𝑋 → ℙ1 explicitly.
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