Birational geometry of smooth families of varieties admitting good minimal models

Behrouz Taji

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arXiv · 2005.01025

Birational geometry of smooth families of varieties admitting good minimal models

Behrouz Taji

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Abstract

In this paper we study families of projective manifolds with good minimal models. After constructing a suitable moduli functor for polarized varieties with canonical singularities, we show that, if not birationally isotrivial, the base spaces of such families support subsheaves of log-pluridifferentials with positive Kodaira dimension. Consequently we prove that, over special base schemes, families of this type can only be birationally isotrivial and, as a result, confirm a conjecture of Kebekus and Kov\'acs.

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Behrouz Taji. 2020-05-03. Birational geometry of smooth families of varieties admitting good minimal models. https://arxiv.org/abs/2005.01025

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