Kaehler manifolds with numerically effective Ricci class and maximal first Betti number are tori
classification
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betticlasseffectivefirstnumbernumericallyricciahler
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Let M be an n-dimensional K\"ahler manifold with numerically effective Ricci class. In this note we prove that, if the first Betti number b_1(M)=2n, then M is biholomorphic to the complex torus T^n_C.
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