A logarithmic $\bar{\partial}$-equation on a compact Kähler manifold associated to a smooth divisor
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866916740379705344 |
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| author | Wan, Xueyuan |
| author_facet | Wan, Xueyuan |
| contents | In this paper, we solve a logarithmic $\bar{\partial}$-equation on a compact Kähler manifold associated to a smooth divisor by using the cyclic covering trick. As applications, we discuss the closedness of logarithmic forms, injectivity theorems and obtain a kind of degeneration of spectral sequence at $E_1$, and we also prove that the pair $(X,D)$ has unobstructed deformations for any smooth divisor $D\in|-2K_X|$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1805_11920 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | A logarithmic $\bar{\partial}$-equation on a compact Kähler manifold associated to a smooth divisor Wan, Xueyuan Algebraic Geometry Complex Variables Differential Geometry In this paper, we solve a logarithmic $\bar{\partial}$-equation on a compact Kähler manifold associated to a smooth divisor by using the cyclic covering trick. As applications, we discuss the closedness of logarithmic forms, injectivity theorems and obtain a kind of degeneration of spectral sequence at $E_1$, and we also prove that the pair $(X,D)$ has unobstructed deformations for any smooth divisor $D\in|-2K_X|$. |
| title | A logarithmic $\bar{\partial}$-equation on a compact Kähler manifold associated to a smooth divisor |
| topic | Algebraic Geometry Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/1805.11920 |