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Instanton sheaves and representations of quivers

Part of: Representation theory of rings and algebras Families, fibrations Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  04 September 2020

M. Jardim  and
D. D. Silva
M. Jardim
Affiliation:
Departamento de Matemática, IMECC - UNICAMP, Rua Sérgio Buarque de Holanda, 651, Campinas, São Paulo13083-970, Brazil (jardim@ime.unicamp.br)
D. D. Silva
Affiliation:
DMA – UFS, Avenida Marechal Rondon S/N, São Cristovão, Sergipe, Brazil (ddsilva@ufs.br)
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Abstract

We study the moduli space of rank 2 instanton sheaves on ℙ3 in terms of representations of a quiver consisting of three vertices and four arrows between two pairs of vertices. Aiming at an alternative compactification for the moduli space of instanton sheaves, we show that for each rank 2 instanton sheaf, there is a stability parameter θ for which the corresponding quiver representation is θ-stable (in the sense of King), and that the space of stability parameters has a non-trivial wall-and-chamber decomposition. Looking more closely at instantons of low charge, we prove that there are stability parameters with respect to which every representation corresponding to a rank 2 instanton sheaf of charge 2 is stable and provide a complete description of the wall-and-chamber decomposition for representation corresponding to a rank 2 instanton sheaf of charge 1.

Keywords

instanton sheavesrepresentations of quiversmoduli spaceswall-crossing

MSC classification

Primary: 14D20: Algebraic moduli problems, moduli of vector bundles
Secondary: 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli 16G20: Representations of quivers and partially ordered sets
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 4 , November 2020 , pp. 984 - 1004
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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