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Abstract: In this lecture compute the horizontal Vafa-Witten invariants, by using Mochizuki's formula, which allows to reduce the computation to Hilbert schemes of points.
Then one can localization in a very similar way as for the vertical Vafa-Witten invariants. This computation confirms some of the predictions of S-duality in ranks 2 and 3. Furthermore, combining with the computations of $S$-duality we predict the generating functions for the horizontal Vafa-Witten invariants in rank at most 5. |
ICTP/IGAP Algebraic Geometry Seminar: Mochizuki's formula and the horizontal Vafa-Witten invariants
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