New moduli spaces of one-dimensional sheaves on ${\mathbb{P}}^3$

Abstract

We define a one-dimensional family of "Euler" stability conditions on ${\mathbb{P}}^n$ which are conjectured to converge to Gieseker stability for coherent sheaves. Here, we focus on ${\mathbb{P}}^3$, first identifying Euler stability conditions with double-tilt stability conditions, and then we consider moduli of one-dimensional sheaves, proving some asymptotic results, boundedness for walls, and then explicitly computing walls and wall-crossings for sheaves supported on rational curves of degrees $3$ and $4$.

References in corpus (1)

• Walls and asymptotics for Bridgeland stability conditions on 3-folds