A survey on rational curves on complex surfaces

Abstract

In this survey we discuss the problem of the existence of rational curves on complex surfaces, both in the Kähler and non-Kähler 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.

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

Cited by in corpus (1)

• Aspherical Complex Surfaces, the Singer Conjecture, and Gromov-Lück Inequality $\chi \ge |\sigma |$