English

On the geometric P=W conjecture

Algebraic Geometry 2022-05-18 v4

Abstract

We formulate the geometric P=W conjecture for singular character varieties. We establish it for compact Riemann surfaces of genus one, and obtain partial results in arbitrary genus. To this end, we employ non-Archimedean, birational and degeneration techniques to study the topology of the dual boundary complex of certain character varieties. We also clarify the relation between the geometric and the cohomological P=W conjectures.

Keywords

Cite

@article{arxiv.1810.11837,
  title  = {On the geometric P=W conjecture},
  author = {Mirko Mauri and Enrica Mazzon and Matthew Stevenson},
  journal= {arXiv preprint arXiv:1810.11837},
  year   = {2022}
}

Comments

33 pages. New appendix. Other minor changes. Final version in Selecta Mathematica

R2 v1 2026-06-23T04:55:00.880Z