Geometry and topology · Oct 6, 2026

Anticanonical nonvanishing in every dimension

If X is a smooth connected complex projective variety and −KX-K_X admits a smooth Hermitian metric with nonnegative curvature, then H0(X,−mKX)≠0H^0(X,-mK_X)\ne0 for some m > 0. Thus smooth semipositivity forces a nonzero section of a positive tensor power of the anticanonical bundle in every dimension.

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