ON HIGGS BUNDLES ON ELLIPTIC SURFACES

Abstract

Let |$\pi : X \rightarrow C$| be a relatively minimal non-isotrivial elliptic surface over the field of complex numbers, where |$g(C) \geq 2$|⁠. In this article, we demonstrate an equivalence between the category of semistable parabolic Higgs bundles on |$C$|⁠, and the category of semistable Higgs bundles on |$X$| with vanishing second Chern class, and determinant a vertical divisor.