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PreprintCC BY 4.0arXiv

Effective Gromov-Witten computations for GKM spaces and a semisimple application

  • Daniel Holmes
  • Giosuè Muratore
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Abstract

We report a major update to our original software GKMtools and record multiple improvements in the computation of Gromov--Witten invariants of GKM spaces. This includes a refined divisor equation that reduces the complexity from exponential to linear in the number of marked points, three tricks to accelerate the computation of curve class relations in the GKM graph, and an implementation of Mihalcea's algorithm for homogeneous varieties using the equivariant quantum Chevalley formula. As an application, we prove that the small quantum cohomology of the type-E generalized Grassmannians E7/P2,E7/P4,E7/P5,E8/P6 is generically semisimple. These are precisely the remaining exceptional Grassmannians for which generic semisimplicity of small quantum cohomology was still unknown.

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Cite

BibTeXRIS
BibTeX
@misc{holmes2026effective,
  title = {{Effective Gromov-Witten computations for GKM spaces and a semisimple application}},
  author = {Daniel Holmes and Giosuè Muratore},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37273},
  eprint = {2610.37273},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37273},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Effective Gromov-Witten computations for GKM spaces and a semisimple application
AU  - Daniel Holmes
AU  - Giosuè Muratore
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37273
UR  - https://arxiv.org/abs/2610.37273
AB  - We report a major update to our original software GKMtools and record multiple improvements in the computation of Gromov--Witten invariants of GKM spaces. This includes a refined divisor equation that reduces the complexity from exponential to linear in the number of marked points, three tricks to accelerate the computation of curve class relations in the GKM graph, and an implementation of Mihalcea's algorithm for homogeneous varieties using the equivariant quantum Chevalley formula. As an application, we prove that the small quantum cohomology of the type-E generalized Grassmannians E_7/P_2,E_7/P_4,E_7/P_5,E_8/P_6 is generically semisimple. These are precisely the remaining exceptional Grassmannians for which generic semisimplicity of small quantum cohomology was still unknown.
ER  -