Kodaira dimension of SU(m)-structures

2025/01/16 by Lorenzo Sillari, Sillari, Lorenzo, Адриано Томассини +1
Mathematics · #32Q60 #53C10 (Primary) 32L05 #53C15 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2501.09612

openalex publication_date 2025/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We study the Kodaira dimension of almost complex manifolds admitting an SU (m)-structure. We introduce the notion of almost complex structure of splitting type and of associated 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 -∞. 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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