2020
Jardim, Marcos; Silva, D. D.
Instanton sheaves and representations of quivers Journal Article
Em: Proceedings of the Edinburgh Mathematical Society, vol. 63, 2020.
Resumo | Links | BibTeX | Tags: instanton sheaves, moduli spaces, representations of quivers, wall-crossing
@article{nokey,
title = {Instanton sheaves and representations of quivers},
author = {Marcos Jardim and D. D. Silva},
url = {https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/abs/instanton-sheaves-and-representations-of-quivers/972F6C19519C40CCDC264A87BD40194D},
doi = {10.1017/S0013091520000292},
year = {2020},
date = {2020-09-04},
journal = {Proceedings of the Edinburgh Mathematical Society},
volume = {63},
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 sheaves, moduli spaces, representations of quivers, wall-crossing},
pubstate = {published},
tppubtype = {article}
}
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.