On the type of generalized hypercomplex structures

Fuente: arXiv
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Main Authors: Fino, Anna, Grantcharov, Gueo
Format: Preprint
Published: 2024
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author Fino, Anna
Grantcharov, Gueo
author_facet Fino, Anna
Grantcharov, Gueo
contents The generalized hypercomplex structures defined within the framework of generalized geometry include hypercomplex and holomorphic symplectic structures as particular cases. They have a $S^2$-family of generalized complex structures, and in this paper we study the types of these structures and the corresponding twistor space. We show that there are generalized hypercomplex structures on the $4n$-dimensional tori, which do not contain a structure of maximal (complex) type. Moreover, we show that the Kodaira-Thurston surface which has a holomorphic symplectic structure, admits also a generalized hypercomplex structure in which all generalized complex structures are of type $1$.
format Preprint
id arxiv_https___arxiv_org_abs_2410_20422
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On the type of generalized hypercomplex structures
Fino, Anna
Grantcharov, Gueo
Differential Geometry
The generalized hypercomplex structures defined within the framework of generalized geometry include hypercomplex and holomorphic symplectic structures as particular cases. They have a $S^2$-family of generalized complex structures, and in this paper we study the types of these structures and the corresponding twistor space. We show that there are generalized hypercomplex structures on the $4n$-dimensional tori, which do not contain a structure of maximal (complex) type. Moreover, we show that the Kodaira-Thurston surface which has a holomorphic symplectic structure, admits also a generalized hypercomplex structure in which all generalized complex structures are of type $1$.
title On the type of generalized hypercomplex structures
topic Differential Geometry
url https://arxiv.org/abs/2410.20422