Global Kodaira Spencer class and Massey products

TL;DR

This paper introduces a new global deformation class concept for semistable complex families over curves, aiding in understanding when such families map onto products with varieties of general type.

Contribution

It defines a supported global deformation class and applies it to characterize when a family admits a finite cover onto a product with a variety of general type.

Findings

Characterizes when a family admits a finite cover onto a product with a general type variety.

Introduces a new notion of supported global deformation class for semistable families.

Provides criteria for the existence of generically finite morphisms onto product spaces.

Abstract

We define a new notion of supported global deformation class for a semistable family of complex varieties over a curve $f\colon X\to B$. We use this notion to study when $X$, possibly up to a finite covering, has a generically finite morphism onto a product $B\times Y$ with $Y$ of general type.