2010/09/16 by Nobuhiro Honda, Honda, Nobuhiro · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.DG
paper · pdf · doi:10.48550/arxiv.1009.3153
31 pages, 5 figures
arxiv created 2010/09/16 · openalex publication_date 2010/09/16 · arxiv updated 2010/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we investigate a family of Moishezon twistor spaces on the connected sum of 4 complex projective planes, which can be regarded as a direct generalization of the twistor spaces on 3CP2 of double solid type studied by Poon and Kreussler-Kurke. These twistor spaces have a natural structure of double covering over a scroll of 2-planes over a conic. We determine the defining equations of the branch divisors in an explicit form, which are very similar to the case of 3CP2. Using these explicit description we compute the dimension of the moduli spaces of these twistor spaces. Also we observe that similarly to the case of 3CP2, these twistor spaces can also be considered as generic Moishezon twistor spaces on 4CP2. We obtain these results by analyzing the anticanonical map of the twistor spaces in detail, which enables us to give an explicit construction of the twistor spaces, up to small resolutions.