Details

Giuseppe Barbaro ^[a], Filippo Fagioli ^[b] and Ángel David Ríos Ortiz ^[c]

A survey on rational curves on complex surfaces

Pages: 505-534
Received: 6 December 2021
Accepted in revised form: 17 January 2023
Mathematics Subject Classification: 32J15 (Primary); 14J99, 53C55 (Secondary).
Keywords: Rational curves, Compact complex surfaces.
Authors address:
[a]: Sapienza Università di Roma, Dipartimento di Matematica "Guido Castelnuovo", Roma, Italy
[b]: Università degli Studi di Firenze, Dipartimento di Matematica e Informatica "Ulisse Dini", Firenze, Italy
[c]: Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany

The authors are supported by GNSAGA of INdAM. The first and second authors are also supported by project PRIN2017 "Real and Complex Manifolds: Topology, Geometry and holomorphic dynamics" (code 2017JZ2SW5).

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.

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