O’Grady spaces and symplectic resolution of moduli spaces of Higgs bundles

Abstract

We describe here a degeneration of the symplectic desingularization of the moduli spaces of topologically trivial G L ( 2 , C ) \mathrm {GL}(2,\mathbb {C}) and S L ( 2 , C ) \mathrm {SL}(2,\mathbb {C}) -Higgs bundles over a hyperelliptic curve, into O’Grady’s ten and six dimensional exceptional examples of irreducible holomorphic symplectic manifolds. Most of this note is a survey of work on these degenerations by Donagi–Ein–Lazarsfeld, de Cataldo–Maulik–Shen and Felisetti–Mauri, although in certain cases we provide details that were missing the previous articles.