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Two-Dimensional Torus Action on the Quadric Threefold and GW-DT-GV Correspondence
Abstract
We compute Gromov--Witten (GW) and Donaldson-Thomas (DT) invariants (including descendant invariants) for local CY $4$-folds over a smooth quadric threefold Q, up to degree $4$. We use the virtual localization formula with respect to a two-dimensional torus action to compute DT invariants. Combining these results with the computation of the J-function of the variety Q, we confirm the correspondence between DT and Gopakumar--Vafa invariants suggested by Cao--Maulik--Toda in genus zero. Based on these results, we predict a genus one BPS invariant on Q.
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BibTeX
@misc{chung2026twodimensional,
title = {{Two-Dimensional Torus Action on the Quadric Threefold and GW-DT-GV Correspondence}},
author = {Kiryong Chung and Sanghyeon Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17964},
eprint = {2610.17964},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17964},
}
RIS
TY - UNPB
TI - Two-Dimensional Torus Action on the Quadric Threefold and GW-DT-GV Correspondence
AU - Kiryong Chung
AU - Sanghyeon Lee
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17964
UR - https://arxiv.org/abs/2610.17964
AB - We compute Gromov--Witten (GW) and Donaldson-Thomas (DT) invariants (including descendant invariants) for local CY $4$-folds over a smooth quadric threefold Q, up to degree $4$. We use the virtual localization formula with respect to a two-dimensional torus action to compute DT invariants. Combining these results with the computation of the J-function of the variety Q, we confirm the correspondence between DT and Gopakumar--Vafa invariants suggested by Cao--Maulik--Toda in genus zero. Based on these results, we predict a genus one BPS invariant on Q.
ER -