Stability conditions and Calabi-Yau fibrations

TL;DR

This paper investigates the structure of stability conditions in triangulated categories linked to three-dimensional Calabi-Yau fibrations, focusing on elliptic and K3 (Abelian) cases, revealing chamber structures and comparisons with fiber stability spaces.

Contribution

It provides a detailed description of stability condition spaces for Calabi-Yau fibrations, introducing chamber structures and fiber comparisons in these geometric contexts.

Findings

Existence of chamber structures similar to movable cones in elliptic fibrations.

Comparison of stability spaces with those of the closed fiber in K3 fibrations.

Insights into the geometric structure of stability conditions in Calabi-Yau fibrations.

Abstract

In this paper, we describe the spaces of stability conditions for the triangulated categories associated to three dimensional Calabi-Yau fibrations. We deal with two cases, the flat elliptic fibrations and smooth K3 (Abelian) fibrations. In the first case, we will see there exist chamber structures similar to those of the movable cone used in birational geometry. In the second case, we will compare the space with the space of stability conditions for the closed fiber of the fibration.