Monge-Ampère equations in big cohomology classes
arXiv:0812.3674
Abstract
We define non-pluripolar products of closed positive currents on a compact Kaehler manifold. We show that a positive non-pluripolar measure can be written in a unique way as the top degree self-intersection (in the non-pluripolar sense) of a closed positive current in given big cohomology class. The solution is shown to have minimal singularities in the sense of Demailly if the measure is regular enough. These results are combined with a fixed point argument to construct singular Kaehler-Einstein volume forms with minimal singularities on varieties of general type.
54 pages. Final version. To appear in Acta Math
References in corpus (6)
- Existence of minimal models for varieties of log general type
- The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension
- A General Non-Vanishing Theorem and an Analytic Proof of the Finite Generation of the Canonical Ring
- Singular Kahler-Einstein metrics
- Intrinsic capacities on compact Kähler manifolds
- An Inequality for Mixed Monge-Ampère measures
Cited by in corpus (13)
- Hölder continuous solutions to Monge-Ampère equations
- Moser-Trudinger type inequalities for complex Monge-Ampère operators and Aubin's "hypothèse fondamentale"
- Stability and regularity of solutions of the Monge-Ampère equation on Hermitian manifolds
- A thermodynamical formalism for Monge-Ampere equations, Moser-Trudinger inequalities and Kahler-Einstein metrics
- Growth of balls of holomorphic sections and energy at equilibrium
- Regularity of plurisubharmonic upper envelopes in big cohomology classes
- On the limit of spectral measures associated to a test configuration
- Solution to a non-Archimedean Monge-Ampère equation
- Fekete points and convergence towards equilibrium measures on complex manifolds
- Pluripotential theory for tropical toric varieties and non-archimedean Monge-Ampére equations
- Restricted volumes and divisorial Zariski decompositions
- Existence of Kahler-Ricci solitons on smoothable Q-Fano varities
- Valuative invariants with higher moments