English

A cone theorem for nef curves

Algebraic Geometry 2011-03-03 v4

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.

Keywords

Cite

@article{arxiv.0807.2294,
  title  = {A cone theorem for nef curves},
  author = {Brian Lehmann},
  journal= {arXiv preprint arXiv:0807.2294},
  year   = {2011}
}

Comments

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

R2 v1 2026-06-21T11:00:32.228Z