A survey on rational curves on complex surfaces

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 ra...

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Bibliographic Details
Published in:arXiv.org 2023-04
Main Authors: Barbaro, Giuseppe, Fagioli, Filippo, Ríos Ortiz, Ángel David
Format: Article
Language:English
Online Access:Get full text
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Summary: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.
ISSN:2331-8422