Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 58 min ago
PreprintarXiv licencearXiv

Universal Curve Counting in Calabi-Yau 4-folds

  • Ivan Karpov
  • Felix Thimm
Open at sourcePDFDOICite

Abstract

Recently, Pardon introduced a universal curve counting framework, which allows him to show that curve counting on 3-folds is "generated" by local curves (in a precise sense). We implement this universal curve counting program for Calabi-Yau 4-folds, where a significant technical difficulty comes from the dependence of the virtual dimension on the genus, which leads to more complicated generators than just local curves. Our main techniques are combinations of deformation-theoretic and homotopy-theoretic methods with an adaptation of Pardon's generic transversality results, which allow us to establish a full set of (computable) generators for CY4 curve counting. As a result, we prove (a slight correction of) the Gromov-Witten/Pandharipande-Thomas correspondence with primary descendents for CY4-folds, formulated by Cao, Maulik, and Toda. From this, we additionally obtain integrality of Gopakumar-Vafa style invariants for CY4-folds, as conjectured by Klemm-Pandharipande.

Related

  1. Counting surfaces on Calabi–Yau 4-folds, I : Foundations
    Younghan Bae, Martijn Kool, Hyeonjun Park
    Geometry & TopologyPeer-reviewedCC BYFull text20 citedGeometry & topologyOpenAlex
  2. On logarithmic Donaldson-Thomas invariants for local Calabi-Yau $4$-folds
    Xiaolong Liu
    arXivPreprintarXiv licenceFull textAlgebra & number theoryMathematical physicsarXiv
  3. Equal-mass sunset integrals and genus-zero local Gromov--Witten theory of Calabi--Yau n-folds
    Hartmut Maennel, Pierre Vanhove
    HALPreprintCC BY 4.0Full textAlgebra & number theoryMathematical physicsHALarXiv
  4. Capillary-gravity water waves with compactly supported vorticity II. Continuation and folds of the solution curve
    Lili Du, Changjun Zou
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. The genus of a curve on Calabi-Yau threefolds
    Vincenzo Di Gennaro, Antonio Rapagnetta, Pietro Sabatino
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{karpov2026universal,
  title = {{Universal Curve Counting in Calabi-Yau 4-folds}},
  author = {Ivan Karpov and Felix Thimm},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02717},
  eprint = {2611.02717},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02717},
}
RIS
TY  - UNPB
TI  - Universal Curve Counting in Calabi-Yau 4-folds
AU  - Ivan Karpov
AU  - Felix Thimm
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02717
UR  - https://arxiv.org/abs/2611.02717
AB  - Recently, Pardon introduced a universal curve counting framework, which allows him to show that curve counting on 3-folds is "generated" by local curves (in a precise sense). We implement this universal curve counting program for Calabi-Yau 4-folds, where a significant technical difficulty comes from the dependence of the virtual dimension on the genus, which leads to more complicated generators than just local curves. Our main techniques are combinations of deformation-theoretic and homotopy-theoretic methods with an adaptation of Pardon's generic transversality results, which allow us to establish a full set of (computable) generators for CY4 curve counting. As a result, we prove (a slight correction of) the Gromov-Witten/Pandharipande-Thomas correspondence with primary descendents for CY4-folds, formulated by Cao, Maulik, and Toda. From this, we additionally obtain integrality of Gopakumar-Vafa style invariants for CY4-folds, as conjectured by Klemm-Pandharipande.
ER  -