Twistors, Hyper-Kaehler Manifolds, and Complex Moduli

2017/02/13 by Claude LeBrun, LeBrun, Claude
Mathematics · #32G05 (primary) #53C26 #53C28 (secondary) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1702.03996

openalex publication_date 2017/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A theorem of Kuranishi tells us that the moduli space of complex structures on any smooth compact manifold is always locally a finite-dimensional space. Globally, however, this is simply not true; we display examples in which the moduli space contains a sequence of regions for which the local dimension tends to infinity. These examples naturally arise from the twistor theory of hyper-Kaehler manifolds.

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