Corpus ID: 119138220

Geometry of folded hypercomplex structures

  title={Geometry of folded hypercomplex structures},
  author={Roger Bielawski and Carolin Peternell},
  journal={arXiv: Differential Geometry},
  • Roger Bielawski, Carolin Peternell
  • Published 2019
  • Mathematics
  • arXiv: Differential Geometry
  • We investigate the geometry of the Kodaira moduli space $M$ of sections of $\pi:Z\to {\mathbb P}^1$, the normal bundle of which is allowed to jump from ${\mathcal O}(1)^{n}$ to ${\mathcal O}(1)^{n-2m}\oplus {\mathcal O}(2)^{m}\oplus {\mathcal O}^{m}$. In particular, we identify the natural assumptions which guarantee that the Obata connection of the hypercomplex part of $M$ extends to a logarithmic connection on $M$. 
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