Abstract
We construct an infinite series of irreducible components of the moduli space of stable rank 3 sheaves on \( ^{3} \) with the zero first Chern class and establish the rationality of the components of this series. We also prove the rationality of the irreducible components of the moduli space of stable rank 2 sheaves on \( ^{3} \) belonging to an infinite subseries of the series of irreducible components described by Jardim, Markushevich, and Tikhomirov.
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Acknowledgment
The author is grateful to the God for the possibility of having this work done, as well as to A.S. Tikhomirov for the idea of the proof of rationality based on the results of Białynicki-Birula and the equivariant resolution of singularities, for the idea to use blowup in the proof of Theorem 1, and other useful discussions. The author is also grateful to the referee for apt remarks.
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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 3, pp. 465–485. https://doi.org/10.33048/smzh.2023.64.303
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Vassiliev, D.A. An Infinite Series of Rational Components of the Moduli Space of Rank 3 Sheaves on \( ^{3} \). Sib Math J 64, 525–541 (2023). https://doi.org/10.1134/S0037446623030035
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DOI: https://doi.org/10.1134/S0037446623030035