Bridgeland walls destabilizing one-dimensional space sheaves

TL;DR

This paper investigates the structure of Bridgeland stability walls for one-dimensional sheaves on threefolds, providing bounds and detailed analysis for specific cases, advancing understanding of stability conditions in algebraic geometry.

Contribution

It introduces bounds for the largest numerical Bridgeland wall and analyzes specific cases with a new computational approach, extending prior work to threefolds.

Findings

Bounds for the largest numerical Bridgeland wall are established.

First known bounds for the Gieseker chamber on threefolds are provided.

Detailed case studies for R=0 and D=3,4 using a Python algorithm.

Abstract

Following the setup proposed by Jardim-Maciocia-Martinez in the case of the projective space, we study some numerical and actual Bridgeland walls for the (twisted) Chern character $v=(-R,0,D,0)$ in certain half-plane of stability conditions, where walls are nested and finite. We give bounds for the largest numerical wall that may appear. When $R=0$, these bounds in particular produce the first known bounds for the Gieseker chamber in the case of a threefold. We also study the cases $R=0$ and $D=3,4$ in detail using a small algorithm in Python.