The aim of this paper is to continue the study of Kodaira dimension for almost complex manifolds, focusing on the case of compact 4-dimensional solvmanifolds without any integrable almost complex structure. According to the classification theory we consider: 3,-1, 4 and 4,λ,-(1+λ) with - 1 < λ < -1 2. For the first solvmanifold we introduce special families of almost complex structures, compute the corresponding Kodaira dimension and show that it is no longer a deformation invariant. Moreover, we prove Ricci flatness of the canonical connection for the almost Kähler structure. Regarding the other two manifolds we compute the Kodaira dimension for certain almost complex structures. Finally, we construct a natural hypercomplex structure providing a twistorial description.

On Kodaira dimension of almost complex 4-dimensional solvmanifolds without complex structures / Cattaneo, A.; Nannicini, A.; Tomassini, A.. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - (2021), p. 2150075.2150075. [10.1142/S0129167X21500750]

On Kodaira dimension of almost complex 4-dimensional solvmanifolds without complex structures

Cattaneo A.;Tomassini A.
2021

Abstract

The aim of this paper is to continue the study of Kodaira dimension for almost complex manifolds, focusing on the case of compact 4-dimensional solvmanifolds without any integrable almost complex structure. According to the classification theory we consider: 3,-1, 4 and 4,λ,-(1+λ) with - 1 < λ < -1 2. For the first solvmanifold we introduce special families of almost complex structures, compute the corresponding Kodaira dimension and show that it is no longer a deformation invariant. Moreover, we prove Ricci flatness of the canonical connection for the almost Kähler structure. Regarding the other two manifolds we compute the Kodaira dimension for certain almost complex structures. Finally, we construct a natural hypercomplex structure providing a twistorial description.
On Kodaira dimension of almost complex 4-dimensional solvmanifolds without complex structures / Cattaneo, A.; Nannicini, A.; Tomassini, A.. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - (2021), p. 2150075.2150075. [10.1142/S0129167X21500750]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2896339
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact