Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

A cone theorem for nef curves


Author: Brian Lehmann
Journal: J. Algebraic Geom. 21 (2012), 473-493
DOI: https://doi.org/10.1090/S1056-3911-2011-00580-8
Published electronically: November 2, 2011
MathSciNet review: 2914801
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Abstract | References | Additional Information

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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Additional Information

Brian Lehmann
Affiliation: Department of Mathematics, Rice University, Houston, Texas 77005
Email: blehmann@rice.edu

DOI: https://doi.org/10.1090/S1056-3911-2011-00580-8
Received by editor(s): July 29, 2009
Received by editor(s) in revised form: November 23, 2010
Published electronically: November 2, 2011
Additional Notes: This material is based upon work supported under a National Science Foundation Graduate Research Fellowship.

American Mathematical Society