Filtrations and torsion pairs in Abramovich Polishchuk's heart
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Accesso online: | |
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| _version_ | 1866910399918505984 |
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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 |