A cone theorem for nef curves

2008/07/15 by Brian Lehmann, Lehmann, Brian
Mathematics · #14E30 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14E30

paper · pdf · doi:10.48550/arxiv.0807.2294

20 pages; v4: improved introduction, several small mistakes corrected

arxiv created 2011/03/02 · arxiv updated 2011/03/03

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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