Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Duality between the pseudoeffective and the movable cone on a projective manifold
HTML articles powered by AMS MathViewer

by David Witt Nyström; with an appendix by Sébastien Boucksom HTML | PDF
J. Amer. Math. Soc. 32 (2019), 675-689 Request permission

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
Similar Articles
  • Retrieve articles in Journal of the American Mathematical Society with MSC (2010): 32L10, 32Q15, 32U05
  • Retrieve articles in all journals with MSC (2010): 32L10, 32Q15, 32U05
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