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@article{Thomas:2023:10.1215/00127094-2022-0059,
author = {Thomas, R and Oh, J},
doi = {10.1215/00127094-2022-0059},
journal = {Duke Mathematical Journal},
pages = {1333--1409},
title = {Counting sheaves on Calabi-Yau 4-folds, I},
url = {http://dx.doi.org/10.1215/00127094-2022-0059},
volume = {172},
year = {2023}
}

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TY  - JOUR
AB  - Borisov-Joyce constructed a real virtual cycle on compactmoduli spaces of stable sheaves on Calabi-Yau 4-folds, using deriveddifferential geometry.We construct an algebraic virtual cycle. A key step is a localisationof Edidin-Graham’s square root Euler class for SOp2n, Cq bundles tothe zero locus of an isotropic section, or to the support of an isotropiccone.We prove a torus localisation formula, making the invariants computable and extending them to the noncompact case when the fixedlocus is compact.We give a K-theoretic refinement by defining K-theoretic square rootEuler classes and their localised versions.In a sequel we prove our invariants reproduce those of Borisov-Joyce.
AU  - Thomas,R
AU  - Oh,J
DO  - 10.1215/00127094-2022-0059
EP  - 1409
PY  - 2023///
SN  - 0012-7094
SP  - 1333
TI  - Counting sheaves on Calabi-Yau 4-folds, I
T2  - Duke Mathematical Journal
UR  - http://dx.doi.org/10.1215/00127094-2022-0059
UR  - http://hdl.handle.net/10044/1/97035
VL  - 172
ER  -

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