English

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 τ\tau-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.

Keywords

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

R2 v1 2026-06-22T20:58:47.101Z