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<p>We construct two infinite series of irreducible components ofthe moduli space of semistable reflexive rank&#xa0;2 sheaveson the three-dimensional complex projective spacewith even and odd first Chern class.In both cases the second and third Chern classesare representable as polynomials in three integer variables.We establish the uniqueness of components in the seriesand describe the relations among these series and previous series of irreducible components.In the series we constructed by the authors in 2024,we find infinite subseries of rational components;these subseries are included into those constructed byJardim, Markushevich, and Tikhomirov in 2017,as well as by Almeida, Jardim, and Tikhomirov in 2022with the use of other constructions of series of components,for which Vassiliev established rationality in 2023.We give an&#xa0;example of moduli space with two irreducible components,one of which belongs toa&#xa0;series of components constructed in this article;while the other,to one previously known.We find the spectra of sheaveswhose equivalence classes constitute these components.</p>

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Series of Components of the Moduli Space of Semistable Reflexive Rank 2 Sheaves on \( {𝕇}^{3} \)

  • 期刊论文

  • 发表日期：

    2025年1月29日

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  • A. A. Kytmanov,
  • N. N. Osipov,
  • S. A. Tikhomirov

摘要

We construct two infinite series of irreducible components ofthe moduli space of semistable reflexive rank 2 sheaveson the three-dimensional complex projective spacewith even and odd first Chern class.In both cases the second and third Chern classesare representable as polynomials in three integer variables.We establish the uniqueness of components in the seriesand describe the relations among these series and previous series of irreducible components.In the series we constructed by the authors in 2024,we find infinite subseries of rational components;these subseries are included into those constructed byJardim, Markushevich, and Tikhomirov in 2017,as well as by Almeida, Jardim, and Tikhomirov in 2022with the use of other constructions of series of components,for which Vassiliev established rationality in 2023.We give an example of moduli space with two irreducible components,one of which belongs toa series of components constructed in this article;while the other,to one previously known.We find the spectra of sheaveswhose equivalence classes constitute these components.