Virtual cycles on projective completions and quantum Lefschetz formula
Algebraic Geometry
2022-02-22 v1
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.
Cite
@article{arxiv.2202.10238,
title = {Virtual cycles on projective completions and quantum Lefschetz formula},
author = {Jeongseok Oh},
journal= {arXiv preprint arXiv:2202.10238},
year = {2022}
}