Anticanonical nonvanishing for smooth projective varieties with smoothly semipositive anticanonical bundle

Theorem 1.1: if $X$ is smooth connected complex projective and $-K_X$ admits a smooth Hermitian metric of semipositive curvature, then $H^0(X,-mK_X)\ne0$ for some $m>0$ . The key intermediate result (Theorem 1.2) gives sections of $aL+bD$ on varieties without holomorphic forms from a finite-volume adjoint metric. Not shown: an effective bound on $m$ , the case $m=1$ (false in general, e.g. Enriques surface times $\mathbb P^1$ ), or nonvanishing when $-K_X$ is only nef or carries a singular semipositive metric.

Exact FrontierDelta

Prior state unknown→proved

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Occurred: Sep 26, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Anticanonical nonvanishing for smooth projective varieties with smoothly semipositive anticanonical bundle · Anticanonical nonvanishing (semipositive)

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Registry verification: unreviewed · announcement · candidate

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VibeMathed record: Anticanonical nonvanishing for smooth projective varieties with smoothly semipositive anticanonical bundle

specialist registry · passed

No independent mathematician has checked this yet. Checked here: the introduction and Theorem 1.1 of 'Anticanonical nonvanishing from smooth semipositivity' were read; the theorem states exactly the displayed question. The posing reference is Yau's 1994 problem list as the manuscript cites it; Yau's text was not obtained, so whether Yau asked for $m=1$ , for a positive multiple, or under nef rather than smooth semipositive hypotheses was not confirmed (the paper's Enriques surface times $\mathbb P^1$ example shows that $m=1$ can fail). The release has no Lean formalization for this family (lean/docs/068.md does not exist at the pinned commit). Companions were skimmed, not refereed.

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Anticanonical nonvanishing for smooth projective varieties with smoothly semipositive anticanonical bundle

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Companion: Invariant anticanonical indices and conversion of twisted differentials

paper · pending