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

MR Author ID:
977848

Email:
blehmann@rice.edu

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.