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Stability of Monge–Ampère Energy Classes

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Abstract

We show that the non-pluripolar product of positive currents is a bimeromorphic invariant. Under some natural assumptions, we show that the (weighted) energy associated with big cohomology classes are also bimeromorphic invariants. We compare the weighted energy functionals of currents with respect to different cohomology classes and establish quantitative estimates between big capacities.

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Acknowledgments

I would like to thank my advisors Vincent Guedj and Stefano Trapani for several useful discussions, for all the time they commit to my research and for their support. I also thank an anonymous referee who helped me clarify Sect. 3.

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Authors and Affiliations

  1. I.M.T., Université Paul Sabatier, 31062, Toulouse Cedex 09, France

    E. Di Nezza

  2. Università di Roma ‘Tor Vergata’, Rome, Italy

    E. Di Nezza

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  1. E. Di Nezza
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Correspondence to E. Di Nezza.

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Communicated by Bo Berndtsson.

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Di Nezza, E. Stability of Monge–Ampère Energy Classes. J Geom Anal 25, 2565–2589 (2015). https://doi.org/10.1007/s12220-014-9526-x

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  • DOI: https://doi.org/10.1007/s12220-014-9526-x

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