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arXiv · 1311.7476

Flops and the S-duality conjecture

Yukinobu Toda
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Abstract

We prove the transformation formula of Donaldson-Thomas (DT) invariants counting two dimensional torsion sheaves on Calabi-Yau 3-folds under flops. The error term is described by the Dedekind eta function and the Jacobi theta function, and our result gives evidence of a 3-fold version of Vafa-Witten's S-duality conjecture. As an application, we prove a blow-up formula of DT type invariants on the total spaces of canonical line bundles on smooth projective surfaces. It gives an analogue of the similar blow-up formula in the original S-duality conjecture by Yoshioka, Li-Qin and Göttsche.

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Yukinobu Toda. 2016-01-28. Flops and the S-duality conjecture. https://doi.org/10.1215/00127094-3129595

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