@article{fbdac33e4e9c4dafb0511a9b5c20a74f,
title = "Virtual cycles of stable (quasi-)maps with fields",
abstract = "We generalize the results of Chang–Li, Kim–Oh and Chang–Li on the moduli of p-fields to the setting of (quasi-)maps to complete intersections in arbitrary smooth Deligne–Mumford stacks with projective coarse moduli. In particular, we show that the virtual cycle of stable (quasi-)maps to a complete intersection can be recovered by the cosection localized virtual cycle of the moduli of p-fields of the ambient space.",
keywords = "Cosection localization, Stable maps with p-fields, Virtual cycle",
author = "Qile Chen and Felix Janda and Rachel Webb",
note = "Funding Information: The first author is partially supported by NSF grant DMS-1700682 . The second author was partially supported by an AMS – Simons travel grant and NSF grants DMS-1901748 and DMS-1638352 . The third author was partially supported by an NSF Postdoctoral Research Fellowship, award number DMS-2002131 . The third author would like to thank Tom Graber, Daniel Halpern-Leistner, Melissa Liu, and Martin Olsson for helpful discussions. The authors thank Jonathan Wise, who shared with us several deformation arguments that greatly simplified the proof; Jack Hall, who provided a crucial lemma for the functoriality needed in Lemma A.2.1 ; Bumsig Kim and Jeongseok Oh, who explained the proof of Lemma 5.0.3 ; and Richard Thomas for suggestions for improving the introduction. The authors are grateful to the AGNES conference and the Casa Matem{\'a}tica Oaxaca which facilitated the completion of this project. Publisher Copyright: {\textcopyright} 2021 The Authors",
year = "2021",
month = jul,
day = "16",
doi = "10.1016/j.aim.2021.107781",
language = "English (US)",
volume = "385",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
}