Twistor lines in the period domain of complex tori
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Twistor lines in the period domain of complex tori

  • Author(s): Buskin, N
  • Izadi, E
  • et al.
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. Furthermore, we show that twistor lines are holomorphic submanifolds of $Compl$, of degree $2$ in the Pl\"ucker embedding of $Compl$.

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