Cohomological stabilization, perverse filtrations, and refined BPS invariants for del Pezzo surfaces
Algebraic Geometry
2024-07-26 v2
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.
Keywords
Cite
@article{arxiv.2406.10004,
title = {Cohomological stabilization, perverse filtrations, and refined BPS invariants for del Pezzo surfaces},
author = {Weite Pi and Junliang Shen and Fei Si and Feinuo Zhang},
journal= {arXiv preprint arXiv:2406.10004},
year = {2024}
}
Comments
Results strengthened, title and authors changed. This version subsumes a major part of arXiv:2406.11512. Comments are welcome!