PreprintCC BY-NC-SA 4.0arXiv
Virtual classes: An introduction with exercises
Abstract
We introduce virtual classes in the sense of Behrend-Fantechi, explaining how these directly generalize Fulton's localized top Chern class. We derive Siebert's formula for a virtual class on any Deligne-Mumford stack with a perfect obstruction theory having a global resolution.
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BibTeX
@misc{lu2026virtual,
title = {{Virtual classes: An introduction with exercises}},
author = {Xuanchun Lu and Rachel Webb},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18454},
eprint = {2609.18454},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18454},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Virtual classes: An introduction with exercises
AU - Xuanchun Lu
AU - Rachel Webb
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18454
UR - https://arxiv.org/abs/2609.18454
AB - We introduce virtual classes in the sense of Behrend-Fantechi, explaining how these directly generalize Fulton's localized top Chern class. We derive Siebert's formula for a virtual class on any Deligne-Mumford stack with a perfect obstruction theory having a global resolution.
ER -