Group actions and irrationality in surface families

TL;DR

This paper investigates how group actions influence the irrationality of surface families, establishing a specialization result that links the degree of irrationality on generic fibers to quotient structures.

Contribution

It introduces a new specialization theorem connecting the degree of irrationality in surface families to quotient by group actions, extending rationality concepts.

Findings

Proves a specialization result for the degree of irrationality.

Links irrationality to quotient by group actions.

Extends rationality concepts to irrationality in surface families.

Abstract

Rationality specializes in families of surfaces, even with mild singularities. In this paper, we study the analogous question for the degree of irrationality. We prove a specialization result when the degree of irrationality on the generic fiber arises from the quotient by a group action.