Logarithmic Kodaira dimension and zeros of holomorphic log-one-forms

Abstract

In this paper, we prove that the zero-locus of any global holomorphic log-one-form on a projective log-smooth pair $\left(X,D\right)$ of log-general type must be non-empty. Applying this result, we give an answer to the algebraic hyperbolicity part of Shafarevich's conjecture, with the generic fiber being Kawamata-log-terminal (klt) and of log-general type.

22 pages, Comments welcome

References in corpus (1)

• Fibration of log-general type space over quasi-abelian varieties

Cited by in corpus (1)

• Hyperbolicity of bases of log Calabi-Yau families