Monodromy action of mirror stops for toric Calabi-Yau surfaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913076320665600 |
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| author | Barbieri, Michela Hanlon, Andrew Hicks, Jeff |
| author_facet | Barbieri, Michela Hanlon, Andrew Hicks, Jeff |
| contents | Mirror symmetry predicts an action by the fundamental group of a conjectural stringy Kähler moduli space on the derived category of an algebraic variety. For a toric variety, a model for this space is understood, but constructing the action is still an open problem in general. We propose that this action can be studied on the $A$-side via a moduli space of Legendrians isotopic to the FLTZ Legendrian. For the $A_{n-1}$ singularity, we construct an annular braid-group action on the corresponding partially wrapped Fukaya category by exact autoequivalences. The standard braid subgroup recovers the Seidel--Thomas action on the derived category, while the additional annular generator corresponds to tensor product with $\mathcal O(-1)$.
We additionally extend the Floer theoretic approach to homological mirror symmetry for toric varities to the setting of semiprojective toric Deligne-Mumford stacks over an arbitrary field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27615 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Monodromy action of mirror stops for toric Calabi-Yau surfaces Barbieri, Michela Hanlon, Andrew Hicks, Jeff Symplectic Geometry Algebraic Geometry 53D37, 14M25, 14F08, 14L24 Mirror symmetry predicts an action by the fundamental group of a conjectural stringy Kähler moduli space on the derived category of an algebraic variety. For a toric variety, a model for this space is understood, but constructing the action is still an open problem in general. We propose that this action can be studied on the $A$-side via a moduli space of Legendrians isotopic to the FLTZ Legendrian. For the $A_{n-1}$ singularity, we construct an annular braid-group action on the corresponding partially wrapped Fukaya category by exact autoequivalences. The standard braid subgroup recovers the Seidel--Thomas action on the derived category, while the additional annular generator corresponds to tensor product with $\mathcal O(-1)$. We additionally extend the Floer theoretic approach to homological mirror symmetry for toric varities to the setting of semiprojective toric Deligne-Mumford stacks over an arbitrary field. |
| title | Monodromy action of mirror stops for toric Calabi-Yau surfaces |
| topic | Symplectic Geometry Algebraic Geometry 53D37, 14M25, 14F08, 14L24 |
| url | https://arxiv.org/abs/2604.27615 |