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arXiv · 2103.00932

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

Szilard Szabo
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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.

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Szilard Szabo. 2021-03-01. $P=W$ conjecture in lowest degree for rank $2$ over the $5$-punctured sphere. https://arxiv.org/abs/2103.00932

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