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arXiv · 2406.10004

Cohomological stabilization, perverse filtrations, and refined BPS invariants for del Pezzo surfaces

Weite Pi·Junliang Shen·Fei Si·Feinuo Zhang
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Abstract

We prove an asymptotic product formula for the refined BPS invariants associated with a local del Pezzo surface. Our formula governs the cohomological stabilization of the perverse filtration on the intersection cohomology of the moduli space of 1-dimensional semistable sheaves on a del Pezzo surface. Combined with the theory of Fourier transform of Maulik--Shen--Yin, we show that the perverse filtration matches asymptotically with the Chern filtration defined via tautological classes. In the case of the projective plane, our results resolve conjectures of Kononov--Pi--Shen.

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Weite Pi, Junliang Shen, Fei Si, Feinuo Zhang. 2024-06-14. Cohomological stabilization, perverse filtrations, and refined BPS invariants for del Pezzo surfaces. https://arxiv.org/abs/2406.10004

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