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.
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