English

Calabi-Yau threefolds with boundary

Differential Geometry 2024-03-25 v1

Abstract

We develop the deformation theory of Calabi-Yau threefolds, by which we mean 3-dimensional complex manifolds with a nowhere-vanishing holomorphic 3-form, on manifolds with boundary. The boundary data is a closed, real 3-form on the 5-dimensional boundary. In the case of strongly pseudoconvex boundary, we obtain an analogue of Hitchin's local Torelli Theorem for compact manifolds, modulo a finite dimensional obstruction space, which we show is zero in many cases of interest.

Keywords

Cite

@article{arxiv.2403.15184,
  title  = {Calabi-Yau threefolds with boundary},
  author = {Simon Donaldson and Fabian Lehmann},
  journal= {arXiv preprint arXiv:2403.15184},
  year   = {2024}
}
R2 v1 2026-06-28T15:29:52.320Z