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

2025/10/12 by Vassiliev, Danil A.
#14F08 (Secondary) #14J30 (Primary) 14D20 #14J60 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.10608

Abstract

We describe rank 2 Gieseker semistable sheaves E on the Fano threefold X₅ of index 2 and degree 5 with maximal third Chern class c₃(E) for all possible low values of discriminant Δ_H(E)≤ 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 X₅ with maximal c₃ and discriminant big enough.

Citations

• Groups generated by spherical twists on K3 surfaces and full exceptional collections on Fano threefolds
• Determinants, even instantons and Bridgeland stability
• Rank two sheaves with maximal third Chern character in three-dimensional\n projective space
• Stability conditions on Fano threefolds of Picard number one
• The Space of Stability Conditions on Abelian Threefolds, and on some\n Calabi-Yau Threefolds
• Even and odd instanton bundles on Fano threefolds of Picard number one
• Bridgeland Stability conditions on threefolds I: Bogomolov-Gieseker type inequalities
• Stability conditions on curves
• Bundles on the Fano threefold V₅
• Vector bundles on Fano 3-folds without intermediate cohomology

Related

• Stability conditions on Fano threefolds of Picard number one
• Discriminants of stable rank two sheaves on some general type surfaces
• Rank two sheaves with maximal third Chern character in three-dimensional\n projective space
• Bogomolov-Gieseker Type Inequality on Calabi-Yau and Fano 3-folds
• Some examples of tilt-stable objects on threefolds