Kodaira classification conjecture for birationally equivalent elliptic threefolds

Let $X\to B$ be a relatively minimal elliptic threefold with section, and let $\Sigma$ be its stratified discriminant locus. The associated nonabelian gauge algebras and their representations encode the singular fibers over the strata. Kodaira classification conjecture. The Kodaira classification of singular fibers on relatively minimal elliptic surfaces, with section, extends to the class of birationally equivalent relatively minimal elliptic threefolds, by associating to $\Sigma$ the nonabelian gauge algebras and their representations. The claim follows a theorem asserting birational invariance of the algebra and representations for $\mathbb{Q}$-factorial terminal minimal models; the supplied text does not state that the proposed classification is fully established.