Weyl symmetry for curve counting invariants via spherical twists

Tim-Henrik Buelles; Miguel Moreira

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arXiv · 2108.06751

Weyl symmetry for curve counting invariants via spherical twists

Tim-Henrik Buelles·Miguel Moreira

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Abstract

We study the curve counting invariants of Calabi--Yau 3-folds via the Weyl reflection along a ruled divisor. We obtain a new rationality result and functional equation for the generating functions of Pandharipande--Thomas invariants. When the divisor arises as resolution of a curve of $A_1$-singularities, our results match the rationality of the associated Calabi--Yau orbifold. The symmetry on generating functions descends from the action of an infinite dihedral group of derived auto-equivalences, which is generated by the derived dual and a spherical twist. Our techniques involve wall-crossing formulas and generalized DT invariants for surface-like objects.

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Tim-Henrik Buelles, Miguel Moreira. 2021-08-15. Weyl symmetry for curve counting invariants via spherical twists. https://arxiv.org/abs/2108.06751

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