Natural Lie Algebra Bundles on Rank Two S-kähler Manifolds, Abelian Varieties and Moduli of Curves
نویسندگان
چکیده
We study the general properties of rank two s-Kähler manifolds. We present several natural examples of manifolds which can be equipped with this structure with various levels of rigidity: complex tori and abelian varieties, cotangent bundles of smooth manifolds and moduli of pointed elliptic curves. We show how one can obtain natural bundles of Lie algebras on such manifolds, with fibres isomorphic to so(s + 1, s + 1), su(s + 1, s + 1), sl(2s + 2, R) and sl(2s + 2, C). 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.
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