Loop Space Formalism and K-Theoretic Quantum Serre Duality
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913187685728256 |
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| author | Yan, Xiaohan |
| author_facet | Yan, Xiaohan |
| contents | In this paper, we prove the quantum Serre duality for genus-zero K-theoretic permutation-invariant Gromov-Witten theory. The formulation of the theorem relies on an extension to the formalism of loop spaces and big $\mathcal{J}$-functions more intrinsic to quantum K-theory. With the extended formalism, we also arrive at a re-interpretation of the level structures in terms of twisted quantum K-theories. We discuss the torus-equivariant theory in the end, and as an application generalize the K-theoretic quantum Serre duality to non-primitive vector bundles over flag varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03054 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Loop Space Formalism and K-Theoretic Quantum Serre Duality Yan, Xiaohan Algebraic Geometry 14N35 In this paper, we prove the quantum Serre duality for genus-zero K-theoretic permutation-invariant Gromov-Witten theory. The formulation of the theorem relies on an extension to the formalism of loop spaces and big $\mathcal{J}$-functions more intrinsic to quantum K-theory. With the extended formalism, we also arrive at a re-interpretation of the level structures in terms of twisted quantum K-theories. We discuss the torus-equivariant theory in the end, and as an application generalize the K-theoretic quantum Serre duality to non-primitive vector bundles over flag varieties. |
| title | Loop Space Formalism and K-Theoretic Quantum Serre Duality |
| topic | Algebraic Geometry 14N35 |
| url | https://arxiv.org/abs/2401.03054 |