PreprintCC BY-NC-ND 4.0arXiv
A Quadratically Enriched Pushforward for Deligne--Mumford Stacks
Abstract
We define a quadratically enriched pushforward for proper morphisms between smooth, proper Deligne--Mumford stacks over an arbitrary field using Grothendieck--Serre duality. We apply this pushforward to define quadratically enriched Euler classes and Euler numbers of relatively oriented vector bundles on smooth, proper Deligne--Mumford stacks. Finally, we define quadratically enriched fundamental classes for smooth, proper schemes over an arbitrary field, and we use these to propose a definition of quadratically enriched quantum K-invariants when the moduli space of stable maps is smooth, tame, and relatively oriented.
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BibTeX
@misc{bethea2026quadratically,
title = {{A Quadratically Enriched Pushforward for Deligne--Mumford Stacks}},
author = {Candace Bethea and Kirsten Wickelgren},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19423},
eprint = {2609.19423},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19423},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A Quadratically Enriched Pushforward for Deligne--Mumford Stacks
AU - Candace Bethea
AU - Kirsten Wickelgren
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19423
UR - https://arxiv.org/abs/2609.19423
AB - We define a quadratically enriched pushforward for proper morphisms between smooth, proper Deligne--Mumford stacks over an arbitrary field using Grothendieck--Serre duality. We apply this pushforward to define quadratically enriched Euler classes and Euler numbers of relatively oriented vector bundles on smooth, proper Deligne--Mumford stacks. Finally, we define quadratically enriched fundamental classes for smooth, proper schemes over an arbitrary field, and we use these to propose a definition of quadratically enriched quantum K-invariants when the moduli space of stable maps is smooth, tame, and relatively oriented.
ER -