English

A survey on rational curves on complex surfaces

Algebraic Geometry 2023-04-06 v2 Differential Geometry

Abstract

In this survey we discuss the problem of the existence of rational curves on complex surfaces, both in the K\"ahler and non-K\"ahler setup. We systematically go through the Enriques--Kodaira classification of complex surfaces to highlight the different approaches applied to the study of rational curves in each class. We also provide several examples and point out some open problems.

Keywords

Cite

@article{arxiv.2209.04229,
  title  = {A survey on rational curves on complex surfaces},
  author = {Giuseppe Barbaro and Filippo Fagioli and Ángel David Ríos Ortiz},
  journal= {arXiv preprint arXiv:2209.04229},
  year   = {2023}
}

Comments

19 pages, 6 figures, comments are welcome. Version accepted for publication in Riv. Mat. Univ. Parma

R2 v1 2026-06-28T01:00:17.255Z