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arXiv · 0807.2294

A cone theorem for nef curves

Brian Lehmann
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Abstract

Following ideas of V. Batyrev, we prove an analogue of the Cone Theorem for the closed cone of nef curves: an enlargement of the cone of nef curves is the closure of the sum of a K_X-non-negative portion and countably many K_X-negative coextremal rays. An example shows that this enlargement is necessary. We also describe the relationship between K_X-negative faces of this cone and the possible outcomes of the minimal model program.

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Brian Lehmann. 2011-03-02. A cone theorem for nef curves. https://arxiv.org/abs/0807.2294

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