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15 September 2015 Flops and the S-duality conjecture
Yukinobu Toda
Duke Math. J. 164(12): 2293-2339 (15 September 2015). DOI: 10.1215/00127094-3129595

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 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.

Citation

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Yukinobu Toda. "Flops and the S-duality conjecture." Duke Math. J. 164 (12) 2293 - 2339, 15 September 2015. https://doi.org/10.1215/00127094-3129595

Information

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

zbMATH: 1331.14055
MathSciNet: MR3397387
Digital Object Identifier: 10.1215/00127094-3129595

Subjects:
Primary: 14N35
Secondary: 18E30

Rights: Copyright © 2015 Duke University Press

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Vol.164 • No. 12 • 15 September 2015
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