Quantum $K$-invariants via Quot schemes II
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909417780281344 |
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| author | Sinha, Shubham Zhang, Ming |
| author_facet | Sinha, Shubham Zhang, Ming |
| contents | We derive a $K$-theoretic analogue of the Vafa--Intriligator formula, computing the (virtual) Euler characteristics of vector bundles over the Quot scheme that compactifies the space of degree $d$ morphisms from a fixed projective curve to the Grassmannian $\mathrm{Gr}(r,N)$. As an application, we deduce interesting vanishing results, used in Part I (arXiv:2406.12191) to study the quantum $K$-ring of $\mathrm{Gr}(r,N)$. In the genus-zero case, we prove a simplified formula involving Schur functions, consistent with the Borel-Weil-Bott theorem in the degree-zero setting. These new formulas offer a novel approach for computing the structure constants of quantum $K$-products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23486 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum $K$-invariants via Quot schemes II Sinha, Shubham Zhang, Ming Algebraic Geometry Representation Theory 14N35, 14N10, 19E08, 14M15 We derive a $K$-theoretic analogue of the Vafa--Intriligator formula, computing the (virtual) Euler characteristics of vector bundles over the Quot scheme that compactifies the space of degree $d$ morphisms from a fixed projective curve to the Grassmannian $\mathrm{Gr}(r,N)$. As an application, we deduce interesting vanishing results, used in Part I (arXiv:2406.12191) to study the quantum $K$-ring of $\mathrm{Gr}(r,N)$. In the genus-zero case, we prove a simplified formula involving Schur functions, consistent with the Borel-Weil-Bott theorem in the degree-zero setting. These new formulas offer a novel approach for computing the structure constants of quantum $K$-products. |
| title | Quantum $K$-invariants via Quot schemes II |
| topic | Algebraic Geometry Representation Theory 14N35, 14N10, 19E08, 14M15 |
| url | https://arxiv.org/abs/2410.23486 |