= Semipositive canonical bundle of a submanifold of a complex torus
{title2=$iF_{K_V}\geq0$}
The tangent bundle of a <complex torus> is holomorphically trivial with a flat <Hermitian metric>. Apply the <curvature formula for a holomorphic subbundle> to $TV\subset TM|_V$: its determinant dual $K_V$ has semipositive curvature. For a closed smooth hypersurface, <adjunction for a smooth submanifold> identifies $K_V$ 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.
Back to article page
