Lectures on curves on varieties -- Lisbon, 2009
J\'anos Koll\'ar (Princeton Univ)
TL;DR
This paper provides an introductory overview of the theory of algebraic curves on varieties, covering dimension formulas, properties of uniruled and rationally connected varieties, and their links to symplectic geometry.
Contribution
It offers a concise introduction to key concepts and recent connections in the study of curves on algebraic varieties, including elementary proofs and geometric properties.
Findings
Elementary proof of the dimension formula for the space of curves
Summary of properties of uniruled and rationally connected varieties
Discussion of connections between algebraic geometry and symplectic geometry
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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology