Twistor lines in the period domain of complex tori

Nikolay Buskin, Elham Izadi

Research output: Contribution to journalArticlepeer-review

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 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 Plücker embedding of Compl.

Original languageEnglish
Number of pages27
JournalGeometriae Dedicata
DOIs
Publication statusPublished - 10 Oct 2020

Keywords

  • Complex tori
  • Hyperkähler manifolds
  • Twistor lines
  • Twistor path connectivity
  • Twistor paths
  • Hyperkahler manifolds

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