Arakelov computations in genus 3 curves (Q1826292)

In the article under review the author computes some Arakelov invariants for the family of curves of genus \(3\) \((C_n):Y^4=X^4-(4n-2)X^2Z^2+Z^4\). Using an isogeny of the jacobian of \(C_n\) with the product of three elliptic curves, the author computes the modular height of \(C_n\) and gives a lower bound for the Arakelov self-intersection of the relative dualizing sheaf. This lower bound shows that the self-intersection can be arbitrarily large. For the proofs the reader is referred to the author's thesis (Universitat de Barcelona, 1988).