AI 中文总结
该研究将域上射影概型的稳定条件构造推广到任意基上的射影族，证明其半稳定对象的相对真模空间存在，还补充证明了相关界存在、倾斜稳定比较等多项结果。
AI 中文摘要
我们将域上射影概型的稳定条件构造推广到任意基上的射影族，并证明它们具有半稳定对象的相对真模空间。我们还证明了一系列互补结果：Halpern-Leistner与Robotis猜想的这类稳定条件的质量-Hom界存在；与曲面和三维簇上倾斜稳定的比较；在特定向量丛全空间的支撑导出范畴上的稳定条件构造，包括所有局部卡拉比-丘簇；以及Bondal与Orlov重构定理的简洁新证明。
英文摘要
We extend the construction of stability conditions on projective schemes over a field to projective families over an arbitrary base, and prove that they admit proper relative moduli spaces of semistable objects. We also prove a number of complementary results: the existence of mass-Hom bounds for these stability conditions, as conjectured by Halpern-Leistner and Robotis; a comparison with tilt-stability on surfaces and threefolds; a construction of stability conditions on the supported derived category of total spaces of certain vector bundles, including all local Calabi--Yau varieties; and a simple new proof of Bondal and Orlov's reconstruction theorem.
Comments83 pages
