On the divisor of involutions in an elliptic modular surface

Abstract

Let E → X E \to X be an elliptic modular surface and S S the tangential ruled surface of a projective embedding of X X . The divisor that collects the involutions of the elliptic fibers of E E is precisely the branch locus of E → S E \to S (at least generically). In this paper, we present two theorems that characterize this divisor in terms of the action of the group of modular automorphisms. These results extend work of D. Burns [1].