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The moduli space of torsion-free sheaves with quasi-maximal third Chern class
Abstract
In this paper, we investigate the geometry of the Gieseker moduli space of semistable rank $2$ torsion-free sheaves on ℙ3 with Chern classes (c1, c2, c3) = (−1, c2, c22−2) for c2 ≥ 2. We use the modular Serre correspondence to relate these moduli spaces to spaces of pairs and to suitable Hilbert schemes of one-dimensional subschemes in ℙ3. For c2 ≥ 4, we prove that the moduli space is irreducible of dimension c22+3c2+5. For the case c2 = 3, relying on a known geometric description of a relevant Hilbert scheme, we show that the moduli space ℳ(−1,3,7) consists of exactly two irreducible components, namely the generic component of reflexive sheaves and a T-component, and we prove that their intersection is nonempty.
Related
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- Birational maps of moduli spaces of stable sheaves on a K3 surface induced by Fourier-Mukai transforms
- Stability of representation cohomology sheaves on moduli spaces of bundles
- Limits of Hyperkähler Manifolds and Moduli Spaces of Sheaves on K3 Surfaces
- Degenerations of shifted symplectic moduli stacks of sheaves
BibTeX
@misc{almeida2026moduli,
title = {{The moduli space of torsion-free sheaves with quasi-maximal third Chern class}},
author = {Charles Almeida and Marcos Jardim and Leonardo Oliveira},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32668},
eprint = {2609.32668},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32668},
}
RIS
TY - UNPB
TI - The moduli space of torsion-free sheaves with quasi-maximal third Chern class
AU - Charles Almeida
AU - Marcos Jardim
AU - Leonardo Oliveira
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32668
UR - https://arxiv.org/abs/2609.32668
AB - In this paper, we investigate the geometry of the Gieseker moduli space of semistable rank $2$ torsion-free sheaves on ℙ^3 with Chern classes (c_1, c_2, c_3) = (−1, c_2, c_2^2−2) for c_2 ≥ 2. We use the modular Serre correspondence to relate these moduli spaces to spaces of pairs and to suitable Hilbert schemes of one-dimensional subschemes in ℙ^3. For c_2 ≥ 4, we prove that the moduli space is irreducible of dimension c_2^2+3c_2+5. For the case c_2 = 3, relying on a known geometric description of a relevant Hilbert scheme, we show that the moduli space ℳ(−1,3,7) consists of exactly two irreducible components, namely the generic component of reflexive sheaves and a T-component, and we prove that their intersection is nonempty.
ER -