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arXiv · 2406.17616

Semiorthogonal decompositions of projective spaces from small quantum cohomology

Vanja Zuliani
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Abstract

In a recent article Halpern-Leistner defines the notion of quasi--convergent path in the space of Bridgeland stability conditions. Such a path induces a semiorthogonal decomposition of the derived category. We investigate quasi-convergent paths in the stability manifold of projective spaces and answer positively to two questions posed by Halpern-Leistner. We construct quasi-convergent paths that start from the geometric region of the stability space and whose central charge is given by a fundamental solution of the quantum differential equation. We also construct quasi-convergent paths whose central charges are the quantum cohomology central charges defined by Iritani.

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Vanja Zuliani. 2026-02-26. Semiorthogonal decompositions of projective spaces from small quantum cohomology. https://arxiv.org/abs/2406.17616

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