Minimal models in numerical dimension one

Abstract — v1

We resolve the numerical-dimension-one case of the minimal-model conjecture for smooth connected complex projective varieties of dimension at least three. If $K_X$ is pseudo-effective and $\kappa_\sigma(X,K_X)=1$, with $\kappa_\sigma$ defined by section growth with a fixed ample twist, then $X$ admits a projective $\mathbb Q$-factorial terminal minimal model.