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arXiv · 2204.05465

Exact formulae and Tur\'{a}n inequalities for Vafa-Witten invariants of $K3$ surfaces

Daniel R. Johnston·Joshua Males
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Abstract

We consider three different families of Vafa-Witten invariants of $K3$ surfaces. In each case, the partition function that encodes the Vafa-Witten invariants is given by combinations of twisted Dedekind $\eta$-functions. By utilising known properties of these $\eta$-functions, we obtain exact formulae for each of the invariants and prove that they asymptotically satisfy all higher-order Tur\'{a}n inequalities.

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Daniel R. Johnston, Joshua Males. 2022-04-12. Exact formulae and Tur\'{a}n inequalities for Vafa-Witten invariants of $K3$ surfaces. https://arxiv.org/abs/2204.05465

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