2017/07/18 by Keiji Oguiso, Oguiso, Keiji, Thomas Peternell +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1707.05657
openalex publication_date 2017/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study smooth complex projective 4-folds which are topologically equivalent. First we show that Fano fourfolds are never oriented homeomorphic to Ricci-flat projective fourfolds and that Calabi-Yau manifolds and hyperkähler manifolds in dimension ≥ 4 are never oriented homeomorphic. Finally, we give a coarse classification of smooth projective fourfolds which are oriented homeomorphic to a hyperkähler fourfold which is deformation equivalent to the Hilbert scheme S[2] of two points of a projective K3 surface S. We also present an explicit example of a smooth projective fourfold oriented homeomorphic to S[2], which has positive Kodaira dimension.