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arXiv · 2206.06839

Filtrations and torsion pairs in Abramovich Polishchuk's heart

Yucheng Liu
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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.

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Yucheng Liu. 2022-06-14. Filtrations and torsion pairs in Abramovich Polishchuk's heart. https://arxiv.org/abs/2206.06839

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