2024/03/22 by Simon Donaldson, Donaldson, Simon, Fabian Lehmann +1 · 1 citation
Mathematics · #32T12 #53C26 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2403.15184
openalex publication_date 2024/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.