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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.12413 |
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| _version_ | 1866912712377761792 |
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| author | Halpern-Leistner, Daniel Herrero, Andres Fernandez |
| author_facet | Halpern-Leistner, Daniel Herrero, Andres Fernandez |
| contents | We define a version of stable maps into the classifying stack $B\mathrm{GL}_N$, and develop a corresponding notion of $K$-theoretic Gromov-Witten invariants. In this setting, the evaluation morphisms are not of finite type; the definition of the $K$-theoretic invariants proceeds by constructing a stability stratification of the moduli stack. In the absence of markings, the semistable locus of the stratification recovers moduli spaces of bundles on nodal curves considered by Gieseker, Nagaraj-Seshadri, Schmitt and Kausz.
We also define versions of stable maps into quotient stacks of the form $Z/\mathrm{GL}_N$, where $Z$ is a projective $\mathrm{GL}_N$-scheme. We construct corresponding stability stratifications, whose semistable loci provide new proper moduli spaces of gauged maps from a varying nodal curve into $Z/\mathrm{GL}_N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12413 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum operations on the ring of symmetric functions Halpern-Leistner, Daniel Herrero, Andres Fernandez Algebraic Geometry Mathematical Physics Quantum Algebra 14D23 (Primary), 14N35, 14D20 (Secondary) We define a version of stable maps into the classifying stack $B\mathrm{GL}_N$, and develop a corresponding notion of $K$-theoretic Gromov-Witten invariants. In this setting, the evaluation morphisms are not of finite type; the definition of the $K$-theoretic invariants proceeds by constructing a stability stratification of the moduli stack. In the absence of markings, the semistable locus of the stratification recovers moduli spaces of bundles on nodal curves considered by Gieseker, Nagaraj-Seshadri, Schmitt and Kausz. We also define versions of stable maps into quotient stacks of the form $Z/\mathrm{GL}_N$, where $Z$ is a projective $\mathrm{GL}_N$-scheme. We construct corresponding stability stratifications, whose semistable loci provide new proper moduli spaces of gauged maps from a varying nodal curve into $Z/\mathrm{GL}_N$. |
| title | Quantum operations on the ring of symmetric functions |
| topic | Algebraic Geometry Mathematical Physics Quantum Algebra 14D23 (Primary), 14N35, 14D20 (Secondary) |
| url | https://arxiv.org/abs/2511.12413 |