Twistor lines in the period domain of complex tori

Nikolay Buskin; Elham Izadi

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arXiv · 1806.07831

Twistor lines in the period domain of complex tori

Nikolay Buskin·Elham Izadi

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Abstract

As in the case of irreducible holomorphic symplectic manifolds, the period domain $Compl$ of compact complex tori of even dimension $2n$ contains twistor lines. These are special $2$-spheres parametrizing complex tori whose complex structures arise from a given quaternionic structure. In analogy with the case of irreducible holomorphic symplectic manifolds, we show that the periods of any two complex tori can be joined by a {\em generic} chain of twistor lines. We also prove a criterion of twistor path connectivity of loci in $Compl$ where a fixed second cohomology class stays of Hodge type (1,1). Furthermore, we show that twistor lines are holomorphic submanifolds of $Compl$, of degree $2n$ in the Pl\"ucker embedding of $Compl$.

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BibTeX RIS

Nikolay Buskin, Elham Izadi. 2018-06-20. Twistor lines in the period domain of complex tori. https://arxiv.org/abs/1806.07831

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