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NEW MODULI SPACES OF ONE-DIMENSIONAL SHEAVES ON $\mathbb {P}^3$
Published online by Cambridge University Press: 18 September 2023
Abstract
We define a one-dimensional family of Bridgeland stability conditions on $\mathbb {P}^n$, named “Euler” stability condition. We conjecture that the “Euler” stability condition converges 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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- © The Author(s), 2023. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal
Footnotes
D.M. is currently supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (Grant No. 2020/03499-0).