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- W2024693438 abstract "We define non-pluripolar products of an arbitrary number of closed positive (1, 1)-currents on a compact Kähler manifold X. Given a big (1, 1)-cohomology class α on X (i.e. a class that can be represented by a strictly positive current) and a positive measure μ on X of total mass equal to the volume of α and putting no mass on pluripolar sets, we show that μ can be written in a unique way as the top-degree self-intersection in the non-pluripolar sense of a closed positive current in α. We then extend Kolodziedj’s approach to sup-norm estimates to show that the solution has minimal singularities in the sense of Demailly if μ has L1+ε-density with respect to Lebesgue measure. If μ is smooth and positive everywhere, we prove that T is smooth on the ample locus of α provided α is nef. Using a fixed point theorem, we finally explain how to construct singular Kähler–Einstein volume forms with minimal singularities on varieties of general type." @default.
- W2024693438 created "2016-06-24" @default.
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- W2024693438 date "2010-01-01" @default.
- W2024693438 modified "2023-10-11" @default.
- W2024693438 title "Monge–Ampère equations in big cohomology classes" @default.
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- W2024693438 doi "https://doi.org/10.1007/s11511-010-0054-7" @default.
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