A curve-class corrected Bogomolov-Gieseker inequality on every polarized threefold

Theorem 1.3: for every smooth projective complex threefold $X$ , ample integral $H$ and $B_0\in N^1(X)_{\mathbb Q}$ there are $k\ge0$ rational and $R_*>0$ with $\mathrm{ch}_3^{B_0+bH}(E)\le(a^2/6+k)H^2\mathrm{ch}_1^{B_0+bH}(E)$ for every tilt-semistable $E$ of slope zero, and the uncorrected bound for $a>R_*$ ; no canonical-bundle hypothesis. The same manuscript constructs, on threefolds with trivial canonical bundle, stability conditions with the exact ordinary and square-root-Todd large-volume charges on an open set of twists and polarizations. It does not give explicit constants or prove the uncorrected BMT inequality at all volumes, which is false in general.

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Occurred: Sep 24, 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: A curve-class corrected Bogomolov-Gieseker inequality on every polarized threefold · Corrected BG inequality on threefolds

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VibeMathed record: A curve-class corrected Bogomolov-Gieseker inequality on every polarized threefold

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No independent mathematician has checked this yet. Checked here: Theorem 1.3 (uniform strong inequality) of the manuscript was read against the two cited questions; it gives, for any smooth projective complex threefold, ample integral $H$ and rational $B_0$ , constants $k\in\mathbb Q_{\ge0}$ and $R_*$ such that every finite-slope $\nu_{a,b}$ -semistable object of slope zero satisfies the inequality corrected by $kH^2\cdot\mathrm{ch}_1$ , for all $a>0$ and $b$ , and the uncorrected inequality once $a>R_*$ . The paper itself says it answers these corrected-inequality questions affirmatively. Note the correction class is a multiple of $H^2$ . Not refereed. No Lean formalization in the release.

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A curve-class corrected Bogomolov-Gieseker inequality on every polarized threefold

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Companion: A Gepner stability condition on every smooth quintic threefold

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Bernardara-Macri-Schmidt-Zhao, Bridgeland stability conditions on Fano threefolds (Question 2.4)

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Bernardara-Macri-Schmidt-Zhao, Bridgeland stability conditions on Fano threefolds (Question 2.4) evidence for this event

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A curve-class corrected Bogomolov-Gieseker inequality on every polarized threefold evidence for this event

VibeMathed record: A curve-class corrected Bogomolov-Gieseker inequality on every polarized threefold evidence for this event

Companion: A Gepner stability condition on every smooth quintic threefold evidence for this event

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