Kodaira dimension of $\mathrm{SU}(m)$-structures
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915611244756992 |
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| author | Sillari, Lorenzo Tomassini, Adriano |
| author_facet | Sillari, Lorenzo Tomassini, Adriano |
| contents | We study the Kodaira dimension of almost complex manifolds admitting an $\mathrm{SU} (m)$-structure. We introduce the notion of almost complex structure of splitting type and of associated $\mathrm{SU} (m)$-structure. When the latter is pseudoholomorphic, we provide two constructions that allow to obtain non-invariant almost complex structures with Kodaira dimension $0$, resp.\ with Kodaira dimension $-\infty$. Our results apply, in particular, to complex structures of splitting type and to several almost complex manifolds already well-studied in the literature |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09612 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kodaira dimension of $\mathrm{SU}(m)$-structures Sillari, Lorenzo Tomassini, Adriano Differential Geometry 32Q60, 53C10 (Primary) 32L05, 53C15 (Secondary) We study the Kodaira dimension of almost complex manifolds admitting an $\mathrm{SU} (m)$-structure. We introduce the notion of almost complex structure of splitting type and of associated $\mathrm{SU} (m)$-structure. When the latter is pseudoholomorphic, we provide two constructions that allow to obtain non-invariant almost complex structures with Kodaira dimension $0$, resp.\ with Kodaira dimension $-\infty$. Our results apply, in particular, to complex structures of splitting type and to several almost complex manifolds already well-studied in the literature |
| title | Kodaira dimension of $\mathrm{SU}(m)$-structures |
| topic | Differential Geometry 32Q60, 53C10 (Primary) 32L05, 53C15 (Secondary) |
| url | https://arxiv.org/abs/2501.09612 |