2025/11/25 by Chou, Tzu-Yang
#14F08 (Primary) 14J30 #18E30 #18E40 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2511.20164
Let X ⊂ ℙ4 be a quadric threefold with a single ordinary double point, and let Ku(X) be its Kuznetsov component. In this paper, we construct a weak stability condition σ_\widetildeD' on its categorical resolution \widetildeD' ⊂ Db(\widetildeX), which is compatible with the Verdier localization Rπ_∗ and descends to a Bridgeland stability condition on Ku(X). This can be viewed as a three-dimensional analogue of our previous result. We describe the geometry of the blow-up π\colon \widetildeX \longrightarrow X and obtain two semiorthogonal decompositions of Db(\widetildeX), arising from the projective bundle structure of \widetildeX and from Kuznetsov's categorical resolution. Comparing them, we isolate an admissible subcategory \widetildeD' ⊆ Db(\widetildeX) resolving Ku(X) and show that it admits a full Ext-exceptional collection, from which we construct σ_\widetildeD'.