Natural Lie Algebra bundles on rank two s-Kähler manifolds, abelian varieties and moduli of curves

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We prove that one can obtain natural bundles of Lie algebras on rank two s-Kähler manifolds, whose fibres are isomorphic to so(s+1,s+1), su(s+1,s+1) and sl(2s + 2,\R). In the most rigid case (which includes complex tori and abelian varieties) these bundles have natural flat connections, whose flat global sections act naturally on cohomology. We also present several natural examples of manifolds which can be equipped with an s-Kähler structure with various levels of rigidity: complex tori and abelian varieties, cotangent bundles of smooth manifolds and moduli of pointed elliptic curves.
in v2 a new theorem in Section 8 has been added

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Algebraic Geometry, Differential Geometry, 14M99; 53B35;81R05

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http://salesiana.dossiersoluciones.com/handle/123456789/155193

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0802.1822
 http://arxiv.org/abs/0802.1822

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arXiv