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arXiv · 2502.08762

Quantum spectrum and Gamma structure for standard flips

Yefeng Shen·Mark Shoemaker
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Abstract

We investigate the quantum spectrum and Gamma structure for projective bundles, blow-ups, and standard flips. After restricting the quantum multiplication to the exceptional curve direction, we obtain a decomposition of the quantum cohomology of standard flips into asymptotic Gamma classes. We then show that this decomposition is compatible with the semi-orthogonal decompositions for these spaces constructed in work of Orlov and Belmans-Fu-Raedschelders. The proof involves a sequence of reductions to a local model and the asymptotic behavior of Meijer G-functions.

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Yefeng Shen, Mark Shoemaker. 2025-02-12. Quantum spectrum and Gamma structure for standard flips. https://arxiv.org/abs/2502.08762

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