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PreprintCC BY 4.0arXiv

From $3$-spin to Negative r-spin: Limits of Cohomological Field Theories and Tautological Relations

  • Deniz Genlik
  • Felix Janda
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Abstract

We prove that the negative r-spin tautological relations of Chidambaram--Garcia-Failde--Giacchetto are a consequence of Pixton's $3$-spin relations, for every r≥2, and deduce that they hold in the tautological Chow ring of ℳ̅g,n. In particular, our result for r=2 implies that Kazarian--Norbury K-relations hold in Chow. The proof factors through two essential parts. The first part shows that the tautological relations arising from Chiodo's class imply the negative r-spin relations. This requires an intricate study of limiting behavior of the Givental--Teleman graph contributions. In the second part, we show that the Chiodo relations are a consequence of Pixton's $3$-spin relations as an application of a generalization of Janda's work on tautological relations from CohFTs.

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Cite

BibTeXRIS
BibTeX
@misc{genlik2026from,
  title = {{From $3$-spin to Negative $r$-spin: Limits of Cohomological Field Theories and Tautological Relations}},
  author = {Deniz Genlik and Felix Janda},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.36509},
  eprint = {2609.36509},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.36509},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - From $3$-spin to Negative r-spin: Limits of Cohomological Field Theories and Tautological Relations
AU  - Deniz Genlik
AU  - Felix Janda
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.36509
UR  - https://arxiv.org/abs/2609.36509
AB  - We prove that the negative r-spin tautological relations of Chidambaram--Garcia-Failde--Giacchetto are a consequence of Pixton's $3$-spin relations, for every r≥2, and deduce that they hold in the tautological Chow ring of ℳ̅_g,n. In particular, our result for r=2 implies that Kazarian--Norbury K-relations hold in Chow. The proof factors through two essential parts. The first part shows that the tautological relations arising from Chiodo's class imply the negative r-spin relations. This requires an intricate study of limiting behavior of the Givental--Teleman graph contributions. In the second part, we show that the Chiodo relations are a consequence of Pixton's $3$-spin relations as an application of a generalization of Janda's work on tautological relations from CohFTs.
ER  -