Volume 18, issue 5 (2014)

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Algebraic Nahm transform for parabolic Higgs bundles on $\mathbb{P}^1$

Kürşat Aker and Szilárd Szabó

Geometry & Topology 18 (2014) 2487–2545
Abstract

We formulate the Nahm transform in the context of parabolic Higgs bundles on ${ℙ}^{1}$ and extend its scope in completely algebraic terms. This transform requires parabolic Higgs bundles to satisfy an admissibility condition and allows Higgs fields to have poles of arbitrary order and arbitrary behavior. Our methods are constructive in nature and examples are provided. The extended Nahm transform is established as an algebraic duality between moduli spaces of parabolic Higgs bundles. The guiding principle behind the construction is to investigate the behavior of spectral data near the poles of Higgs fields.

Keywords
parabolic Higgs bundle, integral transform, birational geometry, spectral sheaf
Mathematical Subject Classification 2010
Primary: 14H60
Secondary: 14E05, 14J26