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Two Series of Components of the Moduli Space of Semistable Reflexive Rank 2 Sheaves on the Projective Space

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Abstract

We construct two new infinite series of irreducible components of the moduli space of semistable nonlocally free reflexive rank 2 sheaves on the three-dimensional complex projective space. In the first series the sheaves have an even first Chern class, and in the second series they have an odd one, while the second and third Chern classes can be expressed as polynomials of a special form in three integer variables. We prove the uniqueness of components in these series for the Chern classes given by those polynomials.

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Notes

  1. Henceforth by a generic point of an irreducible component we understand a closed point belonging to some dense open subset of this component.

References

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Acknowledgment

The authors are grateful to the referee for valuable advice and remarks which helped to substantially improve the text.

Funding

This work is supported by the Krasnoyarsk Mathematical Center and financed by the Ministry of Science and Higher Education of the Russian Federation (Agreement 075–02–2023–936).

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Authors and Affiliations

  1. MIREA—Russian Technological University, Moscow, Russia

    A. A. Kytmanov

  2. Siberian Federal University, Krasnoyarsk, Russia

    A. A. Kytmanov & N. N. Osipov

  3. Ushinsky Yaroslavl State Pedagogical University, Yaroslavl, Russia

    S. A. Tikhomirov

Authors
  1. A. A. Kytmanov
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  2. N. N. Osipov
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  3. S. A. Tikhomirov
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Corresponding author

Correspondence to A. A. Kytmanov.

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The authors of this work declare that they have no conflicts of interest.

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, 2024, Vol. 65, No. 1, pp. 115–124. https://doi.org/10.33048/smzh.2024.65.110

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Kytmanov, A.A., Osipov, N.N. & Tikhomirov, S.A. Two Series of Components of the Moduli Space of Semistable Reflexive Rank 2 Sheaves on the Projective Space. Sib Math J 65, 96–105 (2024). https://doi.org/10.1134/S0037446624010105

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  • DOI: https://doi.org/10.1134/S0037446624010105

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