## Duality between the pseudoeffective and the movable cone on a projective manifold

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David Witt Nyström; with an appendix by Sébastien Boucksom
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## Abstract:

We prove a conjecture of Boucksom-Demailly-Păun-Peternell, namely that on a projective manifold $X$ the cone of pseudoeffective classes in $H^{1,1}_{\mathbb {R}}(X)$ is dual to the cone of movable classes in $H^{n-1,n-1}_{\mathbb {R}}(X)$ via the Poincaré pairing. This is done by establishing a conjectured transcendental Morse inequality for the volume of the difference of two nef classes on a projective manifold. As a corollary the movable cone is seen to be equal to the closure of the cone of balanced metrics. In an appendix by Boucksom it is shown that the Morse inequality also implies that the volume function is differentiable on the big cone, and one also gets a characterization of the prime divisors in the non-Kähler locus of a big class via intersection numbers.## References

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## Additional Information

**David Witt Nyström**- Affiliation: Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, SE-412 96 Gothenburg, Sweden
- Email: wittnyst@chalmers.se, danspolitik@gmail.co
**Sébastien Boucksom**- Affiliation: CNRS–CMLS, École Polytechnique, F-91128 Palaiseau Cedex, France
- MR Author ID: 688226
- Email: sebastien.boucksom@polytechnique.edu
- Received by editor(s): April 11, 2017
- Received by editor(s) in revised form: December 6, 2018
- Published electronically: April 11, 2019
- © Copyright 2019 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**32**(2019), 675-689 - MSC (2010): Primary 32L10, 32Q15, 32U05
- DOI: https://doi.org/10.1090/jams/922
- MathSciNet review: 3981985