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On the Homeomorphism Type of Smooth Projective Fourfolds
Keiji Oguiso
,
Thomas Peternell
Abstract
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 $\ge 4$ 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 $K_3$ surface $S$.