Weighted Bott–Chern and Dolbeault cohomology for LCK-manifolds with potential
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- Ornea Liviu
- University of Bucharest, Faculty of Mathematics Institute of Mathematics, Simion Stoilow of the Romanian Academy
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- Verbitsky Misha
- Laboratory of Algebraic Geometry Faculty of Mathematics, National Research University HSE Université Libre de Bruxelles, Département de Mathématique
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- Vuletescu Victor
- University of Bucharest, Faculty of Mathematics
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Abstract
<p>A locally conformally Kähler (LCK) manifold is a complex manifold, with a Kähler structure on its universal covering \tilde M, with the deck transform group acting on \tilde M by holomorphic homotheties. One could think of an LCK manifold as of a complex manifold with a Kähler form taking values in a local system L, called the conformal weight bundle. The L-valued cohomology of M is called Morse–Novikov cohomology; it was conjectured that (just as it happens for Kähler manifolds) the Morse–Novikov complex satisfies the ddc-lemma, which (if true) would have far-reaching consequences for the geometry of LCK manifolds. In particular, this version of ddc-lemma would imply existence of LCK potential on any LCK manifold with vanishing Morse–Novikov class of its L-valued Hermitian symplectic form. The ddc-conjecture was disproved for Vaisman manifolds by Goto. We prove that the ddc-lemma is true with coefficients in a sufficiently general power of L on any Vaisman manifold or LCK manifold with potential.</p>
Journal
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 70 (1), 409-422, 2018
The Mathematical Society of Japan
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Details 詳細情報について
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- CRID
- 1390282680091521152
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- NII Article ID
- 130006334131
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- NII Book ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- NDL BIB ID
- 028781312
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- Text Lang
- en
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed