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The Albanese Map of sGG Manifolds and Self-Duality of the Iwasawa Manifold. (arXiv:1706.09747v1 [math.AG])
来源于:arXiv
We prove that the three-dimensional Iwasawa manifold $X$, viewed as a locally
holomorphically trivial fibration by elliptic curves over its two-dimensional
Albanese torus, is self-dual in the sense that the base torus identifies
canonically with its dual torus under a sesquilinear duality, the Jacobian
torus of $X$, while the fibre identifies with itself. To this end, we derive
elements of Hodge theory for arbitrary sGG manifolds, introduced in earlier
joint work of the author with L. Ugarte, to construct in an explicit way the
Albanese torus and map of any sGG manifold. These definitions coincide with the
classical ones in the special K\"ahler and $\partial\bar\partial$ cases. The
generalisation to the larger sGG class is made necessary by the Iwasawa
manifold being an sGG, non-$\partial\bar\partial$, manifold. The main result of
this paper can be seen as a complement from a different perspective to the
author's very recent work where a non-K\"ahler mirror symmetry of the Iwasawa
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