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<p>Studying the Gieseker–Maruyama moduli spaceof normalized semistable coherent rank&#xa0;3 sheavesof positive second Chern class and nonnegative third Chern classon the projective space&#xa0;<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1520_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$ {𝕇}^{3} $</EquationSource> </InlineEquation>,we find the first example of an&#xa0;irreducible component of this moduli spacewith small values of Chern classesin which the generic sheaf has singularities of mixed dimension:zero- and one-dimensional singularities simultaneously.Previously,some examples of components of moduli of semistable sheaveswith singularities of mixed dimensionwere constructed only for rank&#xa0;2 sheavesby Ivanov and Tikhomirov in&#xa0;2018as well as by Almeida, Jardim, and Tikhomirov in&#xa0;2022.</p>

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Moduli of Rank 3 Semistable Sheaves on the Projective Space \( {𝕇}^{3} \) with Singularities of Mixed Dimension

  • 期刊论文

  • 发表日期：

    2025年1月29日

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  • I. Yu. Lanskikh,
  • A. S. Tikhomirov

摘要

Studying the Gieseker–Maruyama moduli spaceof normalized semistable coherent rank 3 sheavesof positive second Chern class and nonnegative third Chern classon the projective space  $ {𝕇}^{3} $ ,we find the first example of an irreducible component of this moduli spacewith small values of Chern classesin which the generic sheaf has singularities of mixed dimension:zero- and one-dimensional singularities simultaneously.Previously,some examples of components of moduli of semistable sheaveswith singularities of mixed dimensionwere constructed only for rank 2 sheavesby Ivanov and Tikhomirov in 2018as well as by Almeida, Jardim, and Tikhomirov in 2022.