Order one differential equations on nonisotrivial algebraic curves
Algebraic Geometry
2023-10-11 v2 Classical Analysis and ODEs
Logic
Number Theory
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. These are systems whose solutions only have binary algebraic relations between them. Our technique involves developing a theory of -forms, and building connections to deformation theory. This builds on previous work of Buium and Rosen. In our development, we answer several open questions posed by Rosen and Hrushovski-Itai.
Cite
@article{arxiv.1707.08714,
title = {Order one differential equations on nonisotrivial algebraic curves},
author = {Taylor Dupuy and James Freitag and Aaron Royer},
journal= {arXiv preprint arXiv:1707.08714},
year = {2023}
}
Comments
This paper paper is replaced by arXiv:2309.02327, which greatly expands this manuscript