PreprintCC BY 4.0arXiv
GW/PT-correspondence for CY 4-folds-I: Canonical Orientations
Abstract
We build a cohesive topological theory of orientations on moduli stacks for non-compact complex-analytic Calabi-Yau $4$-folds by extending and generalising the work of Joyce and Upmeier, and the work of Bojko. As a result, we get, in particular, canonical family orientations for all moduli spaces of Pandharipande-Thomas pairs. Our proofs use the algebraic topology of mapping spaces representing KU- and KO- theory, as well as some properties of the Lie groups E8 and, surprisingly, HSpin(16). This is part of a joint project with Felix Thimm dedicated to the proof of the GW/PT-correspondence for Calabi-Yau $4$-folds by implementing Pardon's programme in dimension $4$.
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BibTeX
@misc{karpov2026gwptcorrespondence,
title = {{GW/PT-correspondence for CY 4-folds-I: Canonical Orientations}},
author = {Ivan Karpov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02061},
eprint = {2610.02061},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02061},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - GW/PT-correspondence for CY 4-folds-I: Canonical Orientations
AU - Ivan Karpov
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02061
UR - https://arxiv.org/abs/2610.02061
AB - We build a cohesive topological theory of orientations on moduli stacks for non-compact complex-analytic Calabi-Yau $4$-folds by extending and generalising the work of Joyce and Upmeier, and the work of Bojko. As a result, we get, in particular, canonical family orientations for all moduli spaces of Pandharipande-Thomas pairs. Our proofs use the algebraic topology of mapping spaces representing KU- and KO- theory, as well as some properties of the Lie groups E_8 and, surprisingly, HSpin(16). This is part of a joint project with Felix Thimm dedicated to the proof of the GW/PT-correspondence for Calabi-Yau $4$-folds by implementing Pardon's programme in dimension $4$.
ER -