Plane quartics with Jacobians isomorphic to a hyperelliptic Jacobian (Q2706577)

According to Torelli's theorem any smooth projective curve over an algebraically closed field is determined by its polarized Jacobian variety. \textit{G. Humbert} in [Journ. de Math. (5) 6, 279-386 (1900; JFM 31.0455.04)] gave the first example of two non-isomorphic curves (of genus 2) with the same unpolarized Jacobian. Later many more such examples have been given. The present paper constructs for any positive integer \(n\) distinct smooth plane quartics and one hyperelliptic curve of genus 3 such that all \(n+1\) of these curves have isomorphic unpolarized Jacobian variety. The construction produces explicit equations for curves over \(\mathbb{C}\) whose Jacobians are isomorphic as unpolarized abelian varieties.