Ryo Ohashi

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20232026

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math.AG2026

On superspecial hyperelliptic curves of Rosenhain forms

Ryo Ohashi

Any genus- $g$ hyperelliptic curve $C$ defined over an algebraically closed field of characteristic $p \geq 3$ can be written in a Rosenhain form as $y^2 = x(x-1)\prod_{i=1}^{2g-1}(…

math.AG2026

Superspecial plane quintics with large automorphism groups

Ryo Ohashi

In this paper, we study plane quintic curves whose automorphism groups have order greater than 10, as well as those with cyclic automorphism groups of order 8 and 10. The latter tw…

math.AG2026

Generalized Howe curves of genus 4, 5, and 6 with completely decomposable Jacobians

Ryo Ohashi

Superspecial curves are important objects in number theory and algebraic geometry, and the existence in genus $g \geq 4$ remains an open problem for all but finitely many character…

math.AG2026

On superspecial hyperelliptic curves of genus 5 whose automorphism groups contain $(Z /2 Z)^{3}$

Ryo Ohashi, Momonari Kudo

While the numbers of superspecial curves of genus at most 3 are well understood, and several computational approaches have been developed to count superspecial curves of genus 4 wi…

On superspecial hyperelliptic curves of Rosenhain forms

Superspecial plane quintics with large automorphism groups

Generalized Howe curves of genus 4, 5, and 6 with completely decomposable Jacobians

On superspecial hyperelliptic curves of genus 5 whose automorphism groups contain (Z/2Z)3

On superspecial hyperelliptic curves of genus 5 whose automorphism groups contain $(Z /2 Z)^{3}$