$P=W$ conjecture in lowest degree for rank $2$ over the $5$-punctured sphere

Szilard Szabo

$P=W$ conjecture in lowest degree for rank $2$ over the $5$-punctured sphere

Algebraic Geometry 2021-12-21 v2 Differential Geometry

Authors: Szilard Szabo

Abstract

We use abelianization of Higgs bundles away from the ramification divisor and fiducial solutions to analyze the large scale behaviour of Fenchel--Nielsen co-ordinates on the moduli space of rank $2$ Higgs bundles on the Riemann sphere with $5$ punctures. We solve the related Hitchin WKB problem and prove the lowest degree weighted pieces of the $P=W$ conjecture in this case.

Keywords

p=w conjecture rank 2 higgs bundles 5-punctured sphere fenchel-nielsen coordinates hitchin wkb problem abelianization

Cite

@article{arxiv.2103.00932,
  title  = {$P=W$ conjecture in lowest degree for rank $2$ over the $5$-punctured sphere},
  author = {Szilard Szabo},
  journal= {arXiv preprint arXiv:2103.00932},
  year   = {2021}
}

Comments

Substantially revised, title changed, stronger results

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