Some remarks on the Jacobian variety of Picard curves (Q1382739)

\textit{R. D. M. Accola} [Trans. Am. Math. Soc. 283, 423-449 (1984; Zbl 0584.14016)] gave a characterization of Jacobians of trigonal curves of genus \(\geq 4\) by means of vanishing properties of Riemanns theta function on 6-division points. In the paper under review the analogous result is deduced for Picard curves, i.e., curves \(X\) of genus 3 admitting an automorphism \(\sigma\) of order 6 such that the quotient \(X/\sigma\simeq\mathbb{P}^1\).