Vafa-Witten invariants for projective surfaces. II: Semistable case (Q1623087)

A new approach to Vafa-Witten (VM) invariants counting semistable Higgs pairs on a polarized surface is presented. For so-called \(K3\)-surfaces, VW-invariants are calculated in terms of modular forms. The interconnection of the obtained results with the conjectures of \textit{C. Vafa} and \textit{E. Witten} [Nucl. Phys., B 431, No. 1--2, 3--77 (1994; Zbl 0964.81522)] is considered. For Part I, see [the authors, ``Vafa-Witten invariants for projective surfaces. I: Stable case'', Preprint, \url{arXiv:1702.08487}].