Geodesic
Verlinde formulae on complex surfaces: K-theoretic invariants
Forum of Mathematics, Sigma, Tome 9 (2021)

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We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between K-theoretic Donaldson invariants studied by Göttsche and Nakajima-Yoshioka and K-theoretic Vafa-Witten invariants introduced by Thomas and also studied by Göttsche and Kool. We verify our conjectures in many examples (for example, on K3 surfaces). 
@article{10_1017_fms_2020_50,
     author = {L. G\"ottsche and M. Kool and R. A. Williams},
     title = {Verlinde formulae on complex surfaces: {K-theoretic} invariants},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {9},
     year = {2021},
     doi = {10.1017/fms.2020.50},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2020.50/}
}
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L. Göttsche; M. Kool; R. A. Williams. Verlinde formulae on complex surfaces: K-theoretic invariants. Forum of Mathematics, Sigma, Tome 9 (2021). doi: 10.1017/fms.2020.50

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