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arXiv · 1906.01264

Vertical Vafa-Witten invariants

Pieter Ties Allerd Laarakker
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Abstract

We show that \emph{vertical} contributions to (possibly semistable) Tanaka-Thomas-Vafa-Witten invariants are well defined for surfaces with $p_g(S)>0$, partially proving conjectures of \cite{TT2} and \cite{T}. Moreover, we show that such contributions are computed by the same tautological integrals as in the stable case, which we studied in \cite{L}. Using the work of Kiem and Li, we show that stability of universal families of vertical Joyce-Song pairs is controlled by cosections of the obstruction sheaves of such families.

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Pieter Ties Allerd Laarakker. 2019-06-04. Vertical Vafa-Witten invariants. https://arxiv.org/abs/1906.01264

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