Intrinsic mirrors for minimal adjoint orbits and categories of singularities
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866915205622005760 |
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| author | Gasparim, Elizabeth |
| author_facet | Gasparim, Elizabeth |
| contents | I discuss mirrors of Landau-Ginzburg models formed by a minimal semisimple adjoint orbit of $\mathfrak{sl}(n)$ together with a potential obtained via the Cartan-Killing form. I show that the Landau-Ginzburg models produced by the Gross-Siebert recipe give precisely the objects of the desired mirrors.
It is known that Landau-Ginzburg model $LG(2)$ over the semisimple adjoint orbit of $\mathfrak{sl}(2)$ does not have projective mirrors. I prove Homological Mirror Symmetry for $LG(2)$ by constructing a Landau-Ginzburg mirror and showing that its Orlov category of singularities is equivalent to $Fuk(LG(2))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_02471 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Intrinsic mirrors for minimal adjoint orbits and categories of singularities Gasparim, Elizabeth Algebraic Geometry Symplectic Geometry I discuss mirrors of Landau-Ginzburg models formed by a minimal semisimple adjoint orbit of $\mathfrak{sl}(n)$ together with a potential obtained via the Cartan-Killing form. I show that the Landau-Ginzburg models produced by the Gross-Siebert recipe give precisely the objects of the desired mirrors. It is known that Landau-Ginzburg model $LG(2)$ over the semisimple adjoint orbit of $\mathfrak{sl}(2)$ does not have projective mirrors. I prove Homological Mirror Symmetry for $LG(2)$ by constructing a Landau-Ginzburg mirror and showing that its Orlov category of singularities is equivalent to $Fuk(LG(2))$. |
| title | Intrinsic mirrors for minimal adjoint orbits and categories of singularities |
| topic | Algebraic Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2108.02471 |