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- W4300711483 abstract "Let $(M,I,J,K)$ be a hyperkaehler manifold, $dim_R M =4n$. We study positive, Dolbeault-closed $(2p,0)$-forms on $(M,I)$. These forms are quaternionic analogues of the positive $(p,p)$-forms. We construct an injective homomorphism mapping Dolbeault-closed $(2p,0)$-forms to closed $(n+p,n+p)$-forms, and positive $(2p,0)$-forms to positive $(n+p,n+p)$-forms. This construction is used to prove a hyperkaehler version of the classical Skoda-El Mir theorem, which says that a trivial extension of a closed, positive current over a pluripolar set is again closed. We also prove the hyperkaehler version of the Sibony's lemma, showing that a closed, positive $(2p,0)$-form defined outside of a compact complex subvariety $Zsubset (M,I)$, $codim Z > 2p$ is locally integrable in a neighbourhood of $Z$. These results are used to prove polystability of derived direct images of certain coherent sheaves." @default.
- W4300711483 created "2022-10-04" @default.
- W4300711483 creator A5051189898 @default.
- W4300711483 date "2008-01-12" @default.
- W4300711483 modified "2023-09-27" @default.
- W4300711483 title "Positive forms on hyperkahler manifolds" @default.
- W4300711483 doi "https://doi.org/10.48550/arxiv.0801.1899" @default.
- W4300711483 hasPublicationYear "2008" @default.
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