Birational Geometry of Rationally Connected Manifolds via Quasi-lines

Details Birational Geometry of Rationally Connected Manifolds via Quasi-lines Birational Geometry of Rationally Connected Manifolds via Quasi-lines

2005-02-08

arxiv.org/abs/math/0502160v1

Mathematics

Algebraic Geometry

To appear in Proceedings of Siena Conference "Varieties with Unexpected Properties", 2004

Scientific paper

This is, mostly, a survey of results about the birational geometry of rationally connected manifolds, using rational curves analogous to lines in ${\mathbb P}^n$ ({\it quasi-lines}). Various characterizations of a Zariski neighbourhood of a line in ${\mathbb P}^n$ are obtained, some of them being new. Also, methods of formal geometry are applied for deducing results of birational nature.

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