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NEW MODULI SPACES OF ONE-DIMENSIONAL SHEAVES ON $\mathbb {P}^3$

Part of: Families, fibrations

Published online by Cambridge University Press:  18 September 2023

DAPENG MU Open the ORCID record for DAPENG MU [Opens in a new window]
DAPENG MU*
Affiliation:
Instituto de Matemática, Estatística e Computação Científica (IMECC) Universidade Estadual de Campinas (Unicamp) Room 327-328, IMECC, UNICAMP, Rua Sérgio Buarque de Holanda 651 13083-859 Campinas, SP Brazil
*
mudapeng1990@gmail.com
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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 $4$.

MSC classification

Primary: 14D20: Algebraic moduli problems, moduli of vector bundles
Type
Article
Information
Nagoya Mathematical Journal , First View , pp. 1 - 50
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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Footnotes

D.M. is currently supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (Grant No. 2020/03499-0).

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