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Bibliographic Details
Main Author: Liu, Yucheng
Format: Preprint
Published: 2022
Subjects:
Online Access:https://arxiv.org/abs/2206.06839
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author Liu, Yucheng
author_facet Liu, Yucheng
contents We study some abelian subcategories and torsion pairs in Abramovich Polishchuk's heart. And we construct stability conditions on a full triangulated subcategory $\mathcal{D}^{\leq 1}_S$ in $D(X\times S)$, 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.
format Preprint
id arxiv_https___arxiv_org_abs_2206_06839
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Filtrations and torsion pairs in Abramovich Polishchuk's heart
Liu, Yucheng
Algebraic Geometry
We study some abelian subcategories and torsion pairs in Abramovich Polishchuk's heart. And we construct stability conditions on a full triangulated subcategory $\mathcal{D}^{\leq 1}_S$ in $D(X\times S)$, 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.
title Filtrations and torsion pairs in Abramovich Polishchuk's heart
topic Algebraic Geometry
url https://arxiv.org/abs/2206.06839