Isotrivial smooth curves on surfaces

Xi Chen; Frank Gounelas

Isotrivial smooth curves on surfaces

Algebraic Geometry 2026-07-21 v1

Authors: Xi Chen , Frank Gounelas

Abstract

We prove that a smooth projective non-uniruled surface of Picard rank one, generated by an ample and base point free line bundle, cannot be covered by an isotrivial family of smooth curves in the primitive polarisation.

Cite

@article{arxiv.2607.19256,
  title  = {Isotrivial smooth curves on surfaces},
  author = {Xi Chen and Frank Gounelas},
  journal= {arXiv preprint arXiv:2607.19256},
  year   = {2026}
}