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PreprintCC BY-NC-SA 4.0arXiv

Siebert's formula for virtual pullbacks

  • Xuanchun Lu
  • Rachel Webb
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Abstract

For a DM-type morphism of algebraic stacks f : X → Y with a relative perfect obstruction theory 𝔼 → 𝕃X/Y having a global resolution, we give a formula for the induced virtual pullback in terms of 𝔼 and f. We apply our formula to prove functoriality properties of the virtual fundamental class in Gromov-Witten theory.

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Cite

BibTeXRIS
BibTeX
@misc{lu2026sieberts,
  title = {{Siebert's formula for virtual pullbacks}},
  author = {Xuanchun Lu and Rachel Webb},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12213},
  eprint = {2609.12213},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12213},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Siebert's formula for virtual pullbacks
AU  - Xuanchun Lu
AU  - Rachel Webb
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.12213
UR  - https://arxiv.org/abs/2609.12213
AB  - For a DM-type morphism of algebraic stacks f : X → Y with a relative perfect obstruction theory 𝔼 → 𝕃_X/Y having a global resolution, we give a formula for the induced virtual pullback in terms of 𝔼 and f. We apply our formula to prove functoriality properties of the virtual fundamental class in Gromov-Witten theory.
ER  -