Infinitesimal Torelli for elliptic surfaces revisited

Abstract

In this article we give a new proof for the infinitesimal Torelli theorem for minimal elliptic surfaces without multiple fibers with Euler number at least 24 for nonconstant $j$-invariant. In the case of constant $j$-invariant we find a new proof in the case of Euler number at least 72. We also discuss several new counterexamples.