Semipositive canonical bundle of a submanifold of a complex torus
ID: semipositive-canonical-bundle-of-a-submanifold-of-a-complex-torus
The tangent bundle of a complex torus is holomorphically trivial with a flat Hermitian metric. Apply the curvature formula for a holomorphic subbundle to : its determinant dual has semipositive curvature. For a closed smooth hypersurface, adjunction for a smooth submanifold identifies with the restriction of its divisor line bundle. Thus a positive ambient line bundle remains positive on the hypersurface after tensoring by any nonnegative power of the restricted divisor bundle.
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