Vertical Vafa-Witten invariants
Abstract
We show that vertical contributions to (possibly semistable) Tanaka-Thomas-Vafa-Witten invariants are well defined for surfaces with pg(S)>0, partially proving conjectures of TT2 and T. Moreover, we show that such contributions are computed by the same tautological integrals as in the stable case, which we studied in 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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