The Super Mumford Form and Sato Grassmannian
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866916748429623296 |
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| author | Maxwell, Katherine A. |
| author_facet | Maxwell, Katherine A. |
| contents | We describe a supersymmetric generalization of the construction of Kontsevich and Arbarello, De Concini, Kac, and Procesi, which utilizes a relation between the moduli space of curves with the infinite-dimensional Sato Grassmannian. Our main result is the existence of a flat holomorphic connection on the line bundle $λ_{3/2}\otimesλ_{1/2}^{-5}$ on the moduli space of triples: a super Riemann surface, a Neveu-Schwarz puncture, and a formal coordinate system. We also prove a superconformal Noether normalization lemma for families of super Riemann surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_06625 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Super Mumford Form and Sato Grassmannian Maxwell, Katherine A. Mathematical Physics High Energy Physics - Theory Algebraic Geometry Quantum Algebra We describe a supersymmetric generalization of the construction of Kontsevich and Arbarello, De Concini, Kac, and Procesi, which utilizes a relation between the moduli space of curves with the infinite-dimensional Sato Grassmannian. Our main result is the existence of a flat holomorphic connection on the line bundle $λ_{3/2}\otimesλ_{1/2}^{-5}$ on the moduli space of triples: a super Riemann surface, a Neveu-Schwarz puncture, and a formal coordinate system. We also prove a superconformal Noether normalization lemma for families of super Riemann surfaces. |
| title | The Super Mumford Form and Sato Grassmannian |
| topic | Mathematical Physics High Energy Physics - Theory Algebraic Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2002.06625 |