We study abelian subcategories and torsion pairs in Abramovich–Polishchuk’s heart.And we apply the construction from Liu(J Reine Angew Math 770:135–157,2021)on a full triangulated subcategory D_(S)^(≤1)in D(X×...We study abelian subcategories and torsion pairs in Abramovich–Polishchuk’s heart.And we apply the construction from Liu(J Reine Angew Math 770:135–157,2021)on a full triangulated subcategory D_(S)^(≤1)in D(X×S),for an arbitrary smooth projective variety S.We also define a notion of l-th level stability,which is a generalization of the slope stability and the Gieseker stability.We show that for any object E in Abramovich–Polishchuk’s heart,there is a unique filtration whose factors are l-th level semistable,and the phase vectors are decreasing in a lexicographic order.展开更多
文摘We study abelian subcategories and torsion pairs in Abramovich–Polishchuk’s heart.And we apply the construction from Liu(J Reine Angew Math 770:135–157,2021)on a full triangulated subcategory D_(S)^(≤1)in D(X×S),for an arbitrary smooth projective variety S.We also define a notion of l-th level stability,which is a generalization of the slope stability and the Gieseker stability.We show that for any object E in Abramovich–Polishchuk’s heart,there is a unique filtration whose factors are l-th level semistable,and the phase vectors are decreasing in a lexicographic order.
基金Supported by NNSF of China(11071040)the NSF of Fujian Province(2010J01001)+1 种基金the Education Committee Foundation of Fujian Province(JB11121)the foundation of research and development of Fujian University of Technology(GY-Z10079)
