Filtrations and torsion pairs in Abramovich Polishchuk's heart
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2022
- DOI:
- 10.48550/arXiv.2206.06839
- arXiv:
- arXiv:2206.06839
- Bibcode:
- 2022arXiv220606839L
- Keywords:
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- Mathematics - Algebraic Geometry
- E-Print:
- Version 2, added a proof of Proposition 2.8