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Moduli of rank two semistable sheaves on rational Fano threefolds of the main series
Alexander S. Tikhomirov, Danil A. Vassiliev
https://arxiv.org/abs/2405.20460

Moduli of rank two semistable sheaves on rational Fano threefolds of the main series
In this paper we investigate the moduli spaces of semistable coherent sheaves of rank two on the projective space $\mathbb{P}^3$ and the following rational Fano manifolds of the main series - the three-dimensional quadric $X_2$, the intersection of two 4-dimensional quadrics $X_4$ and the Fano manifold $X_5$ of degree 5. For the quadric $X_2$, the boundedness of the third Chern class $c_3$ of rank two semistable objects in $\mathrm{D}^b(X_2)$, including sheaves, is proved. An explicit descripti…