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

Abstract

We formulate the Nahm transform in the context of parabolic Higgs bundles on ${\mathbb{P}}^1$ 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.