| # Iitaka subadditivity, variation, and logarithmic additivity | |
| The following describes the scope of the Lean formalization related to the following accompanying paper(s): | |
| - [The reverse logarithmic Kodaira inequality and additivity](../../preprints/The-reverse-logarithmic-Kodaira-inequality-and-additivity-September-26-2026/paper.pdf) | |
| ## Scope | |
| The paper studies logarithmic Kodaira additivity for connected-fiber morphisms of smooth projective reduced simple-normal-crossing pairs that are smooth on all boundary strata away from the base boundary. The linked formalization proves the negative-fiber branch: for a very general base point, if the logarithmic Kodaira dimension of the fiber is $-\infty$, then the total logarithmic Kodaira dimension equals the sum of the base and fiber dimensions and is $-\infty$. Every positive-degree logarithmic pluriform section on the total space then vanishes. | |
| The finite-dimension and negative-base branches of the paper's additivity theorem are outside this selected statement. | |
| ## Comparator links | |
| | Result | Comparator statement | | |
| | --- | --- | | |
| | Logarithmic Kodaira additivity in the negative-fiber branch | [LogKodairaFiberNegative.lean](../ComparatorChallenges/LogKodairaFiberNegative.lean) | | |