On supported deformations and birational isotriviality

TL;DR

This paper investigates conditions under which fibrations with a Kodaira-Spencer class supported on a divisor exhibit birational isotriviality, extending classical results about isomorphic fibers in algebraic geometry.

Contribution

It introduces a birational analogue of known results by analyzing cases where the Kodaira-Spencer class is supported on a divisor, broadening understanding of fiber isotriviality.

Findings

Characterization of birational isotriviality when the Kodaira-Spencer class is divisor-supported

Extension of classical isotriviality results to birational settings

Conditions under which fibers are birationally equivalent

Abstract

It is well known that the general fibers of a fibration $f\colon X\to B$ are isomorphic if the general Kodaira-Spencer class vanishes. In this paper we consider the birational analogue when the general Kodaira-Spencer class is supported on a divisor.