Rank Two Sheaves With Low Discriminant on the Fano Threefold of Index 2 and Degree 5

Danil A. Vassiliev

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arXiv · 2510.10608

Rank Two Sheaves With Low Discriminant on the Fano Threefold of Index 2 and Degree 5

Danil A. Vassiliev

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Abstract

We describe rank 2 Gieseker semistable sheaves $E$ on the Fano threefold $X_5$ of index 2 and degree 5 with maximal third Chern class $c_3(E)$ for all possible low values of discriminant $\overline{\Delta}_H(E)\le 40$. The work uses the theory of tilt-stability and Bridgeland stability conditions on smooth projective threefolds. We also make a conjecture about the rank 2 sheaves on $X_5$ with maximal $c_3$ and discriminant big enough.

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Danil A. Vassiliev. 2025-10-12. Rank Two Sheaves With Low Discriminant on the Fano Threefold of Index 2 and Degree 5. https://arxiv.org/abs/2510.10608

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