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

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

2008-02-13

arxiv.org/abs/0802.1822v2

Mathematics

Algebraic Geometry

in v2 a new theorem in Section 8 has been added

Scientific paper

We prove that one can obtain natural bundles of Lie algebras on rank two s-K\"ahler 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-K\"ahler structure with various levels of rigidity: complex tori and abelian varieties, cotangent bundles of smooth manifolds and moduli of pointed elliptic curves.

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