OpenAI reports anticanonical nonvanishing from smooth semipositivity

For every smooth connected projective complex variety whose anticanonical line bundle has a smooth Hermitian metric with semipositive curvature, some positive anticanonical tensor power has a nonzero global section.

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Understanding the problem

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For every smooth connected projective complex variety whose anticanonical line bundle has a smooth Hermitian metric with semipositive curvature, some positive anticanonical tensor power has a nonzero global section.

Why it matters

If correct, resolves the smooth-semipositivity form of Yau’s anticanonical nonvanishing question in every dimension.

What counts as progress

Does a smoothly semipositive anticanonical bundle have a nonzero section in some positive power?

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