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Compact Complex n-folds with Betti numbers $b_1=b_2=b_n=0$ for $n >3$

Are there known examples of compact complex n-dimensional manifolds with betti numbers $b_1=b_2=b_n=0$ for $n >3$? (The case of $n=3$ is the question of integrable complex structures on homology 6-spheres.)

cv.complex-variables dg.differential-geometry ag.algebraic-geometry

asked Dec 23, 2012 at 17:50

Andrew McHugh