Enumerative geometry via elliptic stable envelope
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929455509798912 |
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| author | Smirnov, Andrey |
| author_facet | Smirnov, Andrey |
| contents | Assume $X$ is a variety for which the elliptic stable envelope exists. In this note we construct natural $q$-difference equations from the elliptic stable envelope of $X$. In examples, these equations coincide with the quantum difference equations, which give a natural $q$-deformation of the Dubrovin connection of $X$. Solutions of the quantum difference equations provide generating functions counting curves in $X$. In this way, our construction connects curve counting and equivariant elliptic cohomology.
This is an overview paper based on the author's talk at the workshop The 16th MSJ-SI: Elliptic Integrable Systems, Representation Theory and Hypergeometric Functions, Tokyo 2023. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05643 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enumerative geometry via elliptic stable envelope Smirnov, Andrey Mathematical Physics High Energy Physics - Theory Algebraic Geometry Number Theory Representation Theory Assume $X$ is a variety for which the elliptic stable envelope exists. In this note we construct natural $q$-difference equations from the elliptic stable envelope of $X$. In examples, these equations coincide with the quantum difference equations, which give a natural $q$-deformation of the Dubrovin connection of $X$. Solutions of the quantum difference equations provide generating functions counting curves in $X$. In this way, our construction connects curve counting and equivariant elliptic cohomology. This is an overview paper based on the author's talk at the workshop The 16th MSJ-SI: Elliptic Integrable Systems, Representation Theory and Hypergeometric Functions, Tokyo 2023. |
| title | Enumerative geometry via elliptic stable envelope |
| topic | Mathematical Physics High Energy Physics - Theory Algebraic Geometry Number Theory Representation Theory |
| url | https://arxiv.org/abs/2408.05643 |