On finiteness of fiber space structures of klt Calabi-Yau pairs in dimension 3

TL;DR

This paper proves that for a fixed three-dimensional klt Calabi-Yau pair, the number of fiber space structures is finite when considering automorphisms, highlighting a finiteness property in algebraic geometry.

Contribution

It establishes the finiteness of fiber space structures for fixed three-dimensional klt Calabi-Yau pairs, a new result in the classification of such pairs.

Findings

Finiteness of fiber space structures for fixed 3D klt Calabi-Yau pairs.

Automorphism group acts with finitely many orbits on fiber structures.

Advances understanding of the structure and classification of Calabi-Yau pairs.

Abstract

We prove that for a fixed klt Calabi-Yau pair $(X,\Delta)$ of dimension $3$, the set of fiber space structures of $X$ is finite up to $Aut(X,\Delta)$.