Abstract
In this paper, we study the compact Kähler manifolds whose tangent bundles are numerically effective and whose anti-Kodaira dimensions are equal to one. LetX be a compact Kähler manifold with nef tangent bundle and semiample anti-canonical bundle. We prove that κ(−K X )=1 if and only if there exists a finite étale coverY→X such thatY≅ℙ1×A, whereA is a complex torus. As a consequence, we are able to improve upon a result of T. Fujiwara [3, 4].
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Zhang, Q. A note on compact Kähler manifolds with nef tangent bundles. Manuscripta Math 85, 89–96 (1994). https://doi.org/10.1007/BF02568186
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DOI: https://doi.org/10.1007/BF02568186