2024/03/08 by Nobuhiro Honda, Jeff Viaclovsky, Honda, Nobuhiro +1
Engineering · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #Dynamics and Control of Mechanical Systems #Electromagnetic Scattering and Analysis #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2403.05035
openalex publication_date 2024/03/08 · openalex created_date 2024/03/13 · openalex updated_date 2026/07/28
Let Z be a compact, connected 3-dimensional complex manifold with vanishing first and second Betti numbers and non-vanishing Euler characteristic. We prove that there is no holomorphic mapping from Z onto any 2-dimensional complex space. In other words, Z can only possibly fiber over a curve. This result applies in particular to a class of threefolds, known as Clemens threefolds, which are diffeomorphic to a connected sum k # (S3 × S3) for k ≥ 2. This result also gives a new restriction on any hypothetical complex structure on the 6-sphere S6.