A family of arithmetic surfaces of genus 3.
The author studies a family of the genus 3 curves defined by \[ C_n: Y^4= X^4- (4n- 2)X^2+ 1 \] from the viewpoint of arithmetical and Arakelov geometry. Firstly, the author shows, using his previous result on the automorphism group of \(C_n\), that the Jacobian of \(C_n\) splits as a product of elliptic curves. Using this fact, he finds the stable models of the curves \(C_n\) and studies their arithmetic and geometric properties. Combining these, the author gives explicit expressions of the modular height and the self-intersecction of the dualizing sheaf of the curves \(C_n\).
self-intersection of the dualizing sheaf
scientific article; zbMATH DE number 2101123