0908.4241Aug 28, 2009Final version to appear under the title "Holomorphic and pseudo-holomorphic curves on rationally connected varieties"

Lectures on curves on varieties -- Lisbon, 2009

János Kollár

Algebraic Geometry Symplectic Geometry

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Abstract

These lectures give a short introduction to the study of curves on algebraic varieties. After an elementary proof of the dimension formula for the space of curves, we summarize the basic properties of uniruled and of rationally connected varieties. At the end, some connections with symplectic geometry are considered.

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