Corpus ID: 237213724

On the geometric P=W conjecture

@inproceedings{Mauri2018OnTG,
  title={On the geometric P=W conjecture},
  author={Mirko Mauri and Enrica Mazzon and Matthew Stevenson},
  year={2018}
}
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. 
1 Citations
Lagrangian fibrations
We review the theory of Lagrangian fibrations of hyperkähler manifolds as initiated by Matsushita [Mat99, Mat01, Mat05]. We also discuss more recent work of Shen–Yin [SY18] and Harder–Li–Shen–YinExpand

References

SHOWING 1-10 OF 54 REFERENCES
Algebraic Geometry and Arithmetic Curves
Introduction 1. Some topics in commutative algebra 2. General Properties of schemes 3. Morphisms and base change 4. Some local properties 5. Coherent sheaves and Cech cohmology 6. Sheaves ofExpand
Constructing local models for Lagrangian torus fibrations
We give a construction of Lagrangian torus fibrations with controlled discriminant locus on certain affine varieties. In particular, we apply our construction in the following ways. We find aExpand
Global geometry on moduli of local systems for surfaces with boundary
  • J. Whang
  • Mathematics
  • Compositio Mathematica
  • 2020
Abstract We show that every coarse moduli space, parametrizing complex special linear rank-2 local systems with fixed boundary traces on a surface with nonempty boundary, is log Calabi–Yau in that itExpand
Metric SYZ conjecture and non-archimedean geometry
We show that assuming a conjecture in non-archimedean geometry, then a metric formulation of the SYZ conjecture can be proved in large generality.
P=W conjectures for character varieties with symplectic resolution
We establish P=W and PI=WI conjectures for character varieties with structural group $\mathrm{GL}_n$ and $\mathrm{SL}_n$ which admit a symplectic resolution, i.e. for genus 1 and arbitrary rank, andExpand
The Geometric P=W Conjecture in the Painlevé Cases via Plumbing Calculus
We use plumbing calculus to prove the homotopy commutativity assertion of the Geometric P=W conjecture in all Painleve cases. We discuss the resulting Mixed Hodge structures on Dolbeault and BettiExpand
Cell decompositions of character varieties
We establish curious Lefschetz property for generic character varieties of Riemann surfaces conjectured by Hausel, Letellier and Rodriguez-Villegas. Our main tool applies directly in the case whenExpand
Hitchin fibrations, abelian surfaces, and the P=W conjecture
We study the topology of Hitchin fibrations via abelian surfaces. We establish the P=W conjecture for genus $2$ curves and arbitrary rank. In higher genus and arbitrary rank, we prove that P=W holdsExpand
London School of Geometry and Number Theory
  • 2019
...
1
2
3
4
5
...