Hypersurface Convexity and Extension of Kähler Forms
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916462513356800 |
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| author | Boudreaux, Blake J. Gupta, Purvi Shafikov, Rasul |
| author_facet | Boudreaux, Blake J. Gupta, Purvi Shafikov, Rasul |
| contents | The following generalization of a result of S. Nemirovski is proved: if $X$ is either a projective or a Stein manifold and $K\subset X$ is a compact sublevel set of a strictly plurisubharmonic function $φ$ defined in a neighborhood of $K$, then $X\setminus K$ is a union of positive divisors if and only if $dd^cφ$ extends to a Hodge form on $X$. For an arbitrary compact subset $K\subsetneq X$, this gives that $X\setminus K$ is a union of positive divisors if and only if $K$ admits a neighbourhood basis of sublevel sets of strictly plurisubharmonic functions with the $dd^c$-extension property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_02132 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hypersurface Convexity and Extension of Kähler Forms Boudreaux, Blake J. Gupta, Purvi Shafikov, Rasul Complex Variables Symplectic Geometry 32E20, 32U05 The following generalization of a result of S. Nemirovski is proved: if $X$ is either a projective or a Stein manifold and $K\subset X$ is a compact sublevel set of a strictly plurisubharmonic function $φ$ defined in a neighborhood of $K$, then $X\setminus K$ is a union of positive divisors if and only if $dd^cφ$ extends to a Hodge form on $X$. For an arbitrary compact subset $K\subsetneq X$, this gives that $X\setminus K$ is a union of positive divisors if and only if $K$ admits a neighbourhood basis of sublevel sets of strictly plurisubharmonic functions with the $dd^c$-extension property. |
| title | Hypersurface Convexity and Extension of Kähler Forms |
| topic | Complex Variables Symplectic Geometry 32E20, 32U05 |
| url | https://arxiv.org/abs/2310.02132 |