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arXiv · 2202.10238

Virtual cycles on projective completions and quantum Lefschetz formula

Jeongseok Oh
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Abstract

For a compact quasi-smooth derived scheme M with (-1)-shifted cotangent bundle N, there are at least two ways to localise the virtual cycle of N to M via torus and cosection localisations, introduced by Jiang-Thomas. We produce virtual cycles on both the projective completion and projectivisation and show the ones on the former push down to Jiang-Thomas cycles and the one on the latter computes the difference. Using similar ideas we give an expression for the difference of the quintic and t-twisted quintic GW invariants of Guo-Janda-Ruan.

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Jeongseok Oh. 2022-02-21. Virtual cycles on projective completions and quantum Lefschetz formula. https://arxiv.org/abs/2202.10238

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