Simpson's geometric P=W conjecture in the Painlev\'e VI case via abelianization

Szilard Szabo

Simpson's geometric P=W conjecture in the Painlev\'e VI case via abelianization

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arxiv 1906.01856 v1 pith:QFXWHHOB submitted 2019-06-05 math.AG

Szilard Szabo This is my paper · ORCID

classification math.AG

keywords abelianizationcaseconjecturegeometricpainlevsimpsonassertionbundles

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We use abelianization of Higgs bundles near infinity to prove the homotopy commutativity assertion of Simpson's geometric P=W conjecture in the Painlev\'e VI case.

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Torus fibers and the weight filtration
math.AG 2019-08 conditional novelty 7.0 of 10

A single real torus inside a log Calabi-Yau complement (or a Calabi-Yau degeneration) computes the odd weight filtration, yielding P=W type results for rational surfaces and K3 surfaces.

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