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Popa's logarithmic additivity conjecture for log-smooth families

Theorem 1.1: under Popa's hypotheses (reduced SNC EE, DD, support inclusion, stratum smoothness over VV), κ(X,KX+E)≤κ(Y,KY+D)+κ(F,KF+EF)\kappa(X,K_X+E)\le\kappa(Y,K_Y+D)+\kappa(F,K_F+E_F), and if either term on the right is −∞-\infty every H0(X,m(KX+E))H^0(X,m(K_X+E)) vanishes; no abundance or good-model hypothesis. With the family's logarithmic subadditivity this gives equality, Corollary 1.2. Either divisor may be zero, which covers additivity for smooth projective morphisms; the paper itself claims only Conjecture 3.9. Not covered: families that are not log-smooth over the open base.

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: Popa's logarithmic additivity conjecture for log-smooth families · Popa's log additivity conjecture

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Registry verification: unreviewed · announcement · candidate

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Unreleased internal OpenAI model
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Lean: negative-fibre branch only (challenge not in formalization.yaml)

lean artifact · pending

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Lean: negative-fibre branch only (challenge not in formalization.yaml) evidence for this event

This event attributed to Unreleased internal OpenAI model

Popa's logarithmic additivity conjecture for log-smooth families parent of this event

Theorem 1.1: under Popa's hypotheses (reduced SNC EE, DD, support inclusion, stratum smoothness over VV), κ(X,KX+E)≤κ(Y,KY+D)+κ(F,KF+EF)\kappa(X,K_X+E)\le\kappa(Y,K_Y+D)+\kappa(F,K_F+E_F), and if either term on the right is −∞-\infty every H0(X,m(KX+E))H^0(X,m(K_X+E)) vanishes; no abundance or good-model hypothesis. With the family's logarithmic subadditivity this gives equality, Corollary 1.2. Either divisor may be zero, which covers additivity for smooth projective morphisms; the paper itself claims only Conjecture 3.9. Not covered: families that are not log-smooth over the open base. parent of this event

Popa's logarithmic additivity conjecture for log-smooth families evidence for this event

Orbifold and logarithmic Iitaka subadditivity evidence for this event

VibeMathed record: Popa's logarithmic additivity conjecture for log-smooth families evidence for this event

Popa, Conjectures on the Kodaira dimension (author version) evidence for this event

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Popa's logarithmic additivity conjecture for log-smooth families — Mathematical Frontier Network