Order one differential equations on nonisotrivial algebraic curves

Abstract

In this paper we provide new examples of geometrically trivial strongly minimal differential algebraic varieties living on nonisotrivial curves over differentially closed fields of characteristic zero. Our technique involves developing a theory of Kodaira-Spencer forms and building connections to deformation theory. In our development, we answer several open questions posed by Rosen and some natural questions about Manin kernels.