Duke Mathematical Journal

Flops and the S-duality conjecture

Yukinobu Toda

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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 the Vafa–Witten 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 and Qin, and Göttsche.

Article information

Duke Math. J., Volume 164, Number 12 (2015), 2293-2339.

Received: 20 December 2013
Revised: 15 October 2014
First available in Project Euclid: 16 September 2015

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Zentralblatt MATH identifier

Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 18E30: Derived categories, triangulated categories

Donaldson–Thomas invariants flops derived category of coherent sheaves


Toda, Yukinobu. Flops and the S-duality conjecture. Duke Math. J. 164 (2015), no. 12, 2293--2339. doi:10.1215/00127094-3129595. https://projecteuclid.org/euclid.dmj/1442364464

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