Order one differential equations on nonisotrivial algebraic curves

TL;DR

This paper introduces new examples of minimal differential algebraic varieties on nonisotrivial algebraic curves, utilizing Kodaira-Spencer forms and deformation theory to address open questions in the field.

Contribution

It develops a novel approach connecting Kodaira-Spencer forms with deformation theory to construct and analyze minimal differential algebraic varieties on nonisotrivial curves.

Findings

Constructed new geometrically trivial strongly minimal varieties

Connected Kodaira-Spencer forms to deformation theory

Answered open questions by Rosen and about Manin kernels

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.