Nowhere Vanishing Holomorphic One-Forms on Varieties of Kodaira Codimension One

Abstract Based on the celebrated result zeros of holomorphic 1-forms complex varieties general type by Popa and Schnell, we study $n$-dimensional Kodaira dimension $n-1$. We show that a minimal smooth projective variety $X$ $\kappa (X)=\dim X-1$ admits 1-form without zero if only there is morphism from to an elliptic curve. Furthermore, for (not necessarily minimal) codimension one, give structure theorem given zero.