Stability Conditions on \mathbb P³

2024/08/01 by Dongjian Wu, Wu, Dongjian, Nantao Zhang +1
Mathematics · #Advanced Mathematical Physics Problems #Algebraic Geometry (math.AG) #Algebraic and Geometric Analysis #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2408.00519

openalex publication_date 2024/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a subset of the space of stability conditions for any projective threefold with an ample polarization that satisfies a certain Bogomolov-Gieseker inequality to refine the result in arXiv:1410.1585. Then, we demonstrate that the global dimension, as defined in arXiv:2008.00282 and arXiv:1807.00469, is 3 for any stability condition on \mathbb P³ constructed in arXiv:1410.1585. Finally, we formulate a conjecture concerning the contractibility of a principal connected component of Stab(\mathbb P³).

Related

• Stability conditions on the canonical line bundle of ℙ³
• The Space of Stability Conditions on Abelian Threefolds, and on some\n Calabi-Yau Threefolds
• Stability conditions, Bogomolov-Gieseker type inequalities and Fano 3-folds
• Bogomolov-Gieseker type inequalities on ruled threefolds
• Stability conditions on fibred threefolds