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

Lorenzo Sillari () and Adriano Tomassini ()
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Lorenzo Sillari: Unità di Matematica e Informatica, Università degli Studi di Parma, Dipartimento di Scienze Matematiche, Fisiche e Informatiche
Adriano Tomassini: Unità di Matematica e Informatica, Università degli Studi di Parma, Dipartimento di Scienze Matematiche, Fisiche e Informatiche

A chapter in Real and Complex Geometry, 2025, pp 291-312 from Springer

Abstract: Abstract We study the Kodaira dimension of almost complex manifolds admitting an SU ( m ) $$\mathrm {SU} (m)$$ -structure. We introduce the notion of almost complex structure of splitting type and of associated SU ( m ) $$\mathrm {SU}(m)$$ -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.

Keywords: Almost complex structure; Canonical bundle; Kodaira dimension; Pseudoholomorphic section; Solvmanifold; SU ( m ) $$\mathrm {SU}(m)$$ -structure; Primary: 32Q60, 53C10; Secondary: 32L05, 53C15 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-92297-8_14

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

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