Perversity equals weight for Painlev\'e spaces
Algebraic Geometry
2021-03-16 v5
Abstract
We provide further evidence to the conjecture of de Cataldo, Hausel and Migliorini, by checking it in the Painlev\'e cases. Namely, we compare the perverse Leray filtration induced by the Hitchin map on the cohomology spaces of the Dolbeault moduli space and the weight filtration on the cohomology spaces of the irregular character variety corresponding to each of the Painlev\'e systems. We find that the two filtrations agree. Along the way, we prove the Geometric conjecture of Katzarkov, Noll, Pandit and Simpson in the Painlev\'e cases, and show that in these cases the Geometric conjecture implies the conjecture.
Keywords
Cite
@article{arxiv.1802.03798,
title = {Perversity equals weight for Painlev\'e spaces},
author = {Szilárd Szabó},
journal= {arXiv preprint arXiv:1802.03798},
year = {2021}
}
Comments
Final version, to appear in Adv. Math., containing the material of 1906.01856