Nahm transformation for parabolic Higgs bundles on the projective line --- case of non-semisimple residues

TL;DR

This paper extends the Nahm transformation for parabolic Higgs bundles on the projective line to include non-semisimple residues, establishing a holomorphic map on moduli spaces through elementary modifications of the Dolbeault complex.

Contribution

It introduces a generalized Nahm transformation for non-semisimple residues, expanding the applicability of the method to broader classes of Higgs bundles.

Findings

Constructed a holomorphic map on moduli spaces for non-semisimple residues

Extended the Nahm transformation to more general parabolic Higgs bundles

Demonstrated the use of elementary modifications of the Dolbeault complex

Abstract

We extend our earlier construction of Nahm transformation for parabolic Higgs bundles on the projective line to solutions with not necessarily semisimple residues and show that it determines a holomorphic mapping on corresponding moduli spaces. The construction relies on suitable elementary modifications of the logarithmic Dolbeault complex.