Some observations about isogenies between $K3$ surfaces

Abstract

Even if there are too many elliptic fibrations to investigate and describe on the singular $K3$ surface $Y_{10}$ of discriminant 72 and belonging to the Apéry-Fermi pencil $(Y_k)$, we find on it many interesting properties. For example some of its elliptic fibrations with 3-torsion section induce by 3-isogeny either an elliptic fibration of $Y_2$, the unique $K3$ surface of discriminant 8, or an elliptic fibration of other $K3$ surfaces of discriminant 72.

48 pages

References in corpus (1)

• The Mahler measure and the L-series of a singular K3-surface