PreprintCC BY-NC-SA 4.0arXiv
Bulk-deformed enumerative mirror symmetry for toric Fano surfaces
Abstract
We prove a version of genus-0 mirror symmetry for toric Fano surfaces at the level of big quantum cohomology. The mirror Landau-Ginzburg model (checkX, W∞) of such a surface X can be defined in terms of counts of Maslov index two tropical or holomorphic discs with bulk insertions. While these mirror LG models are not well-defined, the Jacobian ring Jac(W∞) of the superpotential W∞ is well-defined. We show that Jac(W∞) is isomorphic over the Novikov base to the big quantum cohomology of X using tropical methods, providing a purely algebraic analogue of the cobordism argument used in works of Fukaya-Oh-Ohta-Ono.
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BibTeX
@misc{lu2026bulkdeformed,
title = {{Bulk-deformed enumerative mirror symmetry for toric Fano surfaces}},
author = {Xuanchun Lu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28496},
eprint = {2609.28496},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28496},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Bulk-deformed enumerative mirror symmetry for toric Fano surfaces
AU - Xuanchun Lu
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.28496
UR - https://arxiv.org/abs/2609.28496
AB - We prove a version of genus-0 mirror symmetry for toric Fano surfaces at the level of big quantum cohomology. The mirror Landau-Ginzburg model (checkX, W_∞) of such a surface X can be defined in terms of counts of Maslov index two tropical or holomorphic discs with bulk insertions. While these mirror LG models are not well-defined, the Jacobian ring Jac(W_∞) of the superpotential W_∞ is well-defined. We show that Jac(W_∞) is isomorphic over the Novikov base to the big quantum cohomology of X using tropical methods, providing a purely algebraic analogue of the cobordism argument used in works of Fukaya-Oh-Ohta-Ono.
ER -