Let X be a compact complex manifold with trivial canonical bundle and satisfying the (Formula presented.)-Lemma. We show that the Kuranishi space of X is a smooth universal deformation and that small deformations enjoy the same properties as X. If, in addition, X admits a complex symplectic form, then the local Torelli theorem holds and we obtain some information about the period map. We clarify the structure of such manifolds a little by showing that the Albanese map is a surjective submersion.

$$partial overlinepartial $$ -Complex symplectic and Calabi–Yau manifolds: Albanese map, deformations and period maps / Anthes, Ben; Cattaneo, Andrea; Rollenske, Sönke; Tomassini, Adriano. - In: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. - ISSN 0232-704X. - 54:3(2018), pp. 377-398. [10.1007/s10455-018-9607-3]

$$partial overlinepartial $$ -Complex symplectic and Calabi–Yau manifolds: Albanese map, deformations and period maps

Cattaneo, Andrea;Tomassini, Adriano
2018

Abstract

Let X be a compact complex manifold with trivial canonical bundle and satisfying the (Formula presented.)-Lemma. We show that the Kuranishi space of X is a smooth universal deformation and that small deformations enjoy the same properties as X. If, in addition, X admits a complex symplectic form, then the local Torelli theorem holds and we obtain some information about the period map. We clarify the structure of such manifolds a little by showing that the Albanese map is a surjective submersion.
$$partial overlinepartial $$ -Complex symplectic and Calabi–Yau manifolds: Albanese map, deformations and period maps / Anthes, Ben; Cattaneo, Andrea; Rollenske, Sönke; Tomassini, Adriano. - In: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. - ISSN 0232-704X. - 54:3(2018), pp. 377-398. [10.1007/s10455-018-9607-3]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2843201
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