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

In: Real and Complex Geometry

Author

Listed:
  • 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)

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.

Suggested Citation

  • Lorenzo Sillari & Adriano Tomassini, 2025. "Kodaira Dimension of SU ( m ) $$\mathrm {SU}(\lowercase {m})$$ -structures," Springer Books, in: Liviu Ornea (ed.), Real and Complex Geometry, pages 291-312, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-92297-8_14
    DOI: 10.1007/978-3-031-92297-8_14
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