On the complex Monge–Ampère operator for quasi‐plurisubharmonic functions with analytic singularities

We give a modified, very natural definition for the complex Monge–Ampère operator for an ω‐plurisubharmonic (psh) function φ with analytic singularities on a Kähler manifold (X,ω) of dimension n which has the property ∫X(ω+ddcφ)n=∫Xωn if X is compact. This means that, unlike in the previous definiti...

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Veröffentlicht in:	The Bulletin of the London Mathematical Society 2019-06, Vol.51 (3), p.431-435
1. Verfasser:	Błocki, Zbigniew
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Sprache:	eng
Schlagworte:	32Q15 32S05 (secondary) 32U05 (primary) 32W20
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description	We give a modified, very natural definition for the complex Monge–Ampère operator for an ω‐plurisubharmonic (psh) function φ with analytic singularities on a Kähler manifold (X,ω) of dimension n which has the property ∫X(ω+ddcφ)n=∫Xωn if X is compact. This means that, unlike in the previous definition, no mass is lost here. In fact, the definition works for any smooth (1,1)‐form ω (we need neither closedness nor positivity) and quasi‐psh φ with analytic singularities.
doi_str_mv	10.1112/blms.12239
format	Article
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title	On the complex Monge–Ampère operator for quasi‐plurisubharmonic functions with analytic singularities
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