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Rational curves on varieties. (English) Zbl 1080.14521
Böröczky, Károly jun. (ed.) et al., Higher dimensional varieties and rational points. Lectures of the summer school and conference, Budapest, Hungary, September 3–21, 2001. Berlin: Springer; Budapest: János Bolyai Mathematical Society (ISBN 3-540-00820-9/hbk; 963-9453-02-1). Bolyai Soc. Math. Stud. 12, 13-68 (2003).
Summary: The aim of these notes is to give a introduction to the ideas and techniques of handling rational curves on varieties. The main emphasis is on varieties with many rational curves which are the higher dimensional analogs of rational curves and surfaces. The first six sections closely follow the lectures of J. Kollár given at the summer school “Higher dimensional varieties and rational points”. The notes were written up by C. Araujo and substantially edited later.
For the entire collection see [Zbl 1015.00008].

MSC:
14H50 Plane and space curves
14J26 Rational and ruled surfaces
14H45 Special algebraic curves and curves of low genus
14H10 Families, moduli of curves (algebraic)
14J40 \(n\)-folds (\(n>4\))
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