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arXiv · 2002.00442

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

Dapeng Mu
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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 $4$.

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Dapeng Mu. 2020-02-02. New moduli spaces of one-dimensional sheaves on $\mathbb{P}^3$. https://arxiv.org/abs/2002.00442

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