Kodaira dimension of $\mathrm{SU}(m)$-structures

Lorenzo Sillari; Adriano Tomassini

doi:10.1007/978-3-031-92297-8_14

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arXiv · 2501.09612

Kodaira dimension of $\mathrm{SU}(m)$-structures

Lorenzo Sillari·Adriano Tomassini

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Abstract

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

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Lorenzo Sillari, Adriano Tomassini. 2025-01-16. Kodaira dimension of $\mathrm{SU}(m)$-structures. https://doi.org/10.1007/978-3-031-92297-8_14

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