On covering and quasi-unsplit families of rational curves

Mathematics – Algebraic Geometry

Scientific paper

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13 pages

Scientific paper

We study extremality properties of covering families of rational curves on
projective varieties. Among others, we show that on a normal and Q-factorial
projective variety of dimension at most 4, every covering and quasi-unsplit
family of rational curves generates a geometric extremal ray of the Mori cone.

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