में बचाया:
| मुख्य लेखकों: | , |
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| स्वरूप: | Preprint |
| प्रकाशित: |
2025
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| विषय: | |
| ऑनलाइन पहुंच: | https://arxiv.org/abs/2505.22233 |
| टैग: |
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| _version_ | 1866914337879228416 |
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| author | Bruzzo, Ugo Ruipérez, Daniel Hernández |
| author_facet | Bruzzo, Ugo Ruipérez, Daniel Hernández |
| contents | We review the notion of stable supermap from SUSY curves to a fixed target superscheme, and prove that when the target is (super)projective, stable supermaps are parameterized by a Deligne-Mumford superstack with superschematic and separated diagonal. We characterize the bosonic reduction of this moduli superstack and see that it has a surjective morphism onto the moduli stack of stable maps from spin curves to the bosonic reduction of the target, whose fibers are linear schemes; for this reason, the moduli superstack of stable supermaps is not proper unless such linear schemes reduce to a point. Using Manin-Penkov-Voronov's super Grothendieck-Riemann-Roch theorem we also make a formal computation of the virtual dimension of the moduli superstack, which agrees with the characterization of the bosonic reduction just mentioned and with the dimension formula for the case of bosonic target existing in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22233 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moduli of stable supermaps Bruzzo, Ugo Ruipérez, Daniel Hernández Algebraic Geometry High Energy Physics - Theory Mathematical Physics Primary: 14D23, Secondary: 14A20, 14H10, 14M30, 81T30, 83E30 We review the notion of stable supermap from SUSY curves to a fixed target superscheme, and prove that when the target is (super)projective, stable supermaps are parameterized by a Deligne-Mumford superstack with superschematic and separated diagonal. We characterize the bosonic reduction of this moduli superstack and see that it has a surjective morphism onto the moduli stack of stable maps from spin curves to the bosonic reduction of the target, whose fibers are linear schemes; for this reason, the moduli superstack of stable supermaps is not proper unless such linear schemes reduce to a point. Using Manin-Penkov-Voronov's super Grothendieck-Riemann-Roch theorem we also make a formal computation of the virtual dimension of the moduli superstack, which agrees with the characterization of the bosonic reduction just mentioned and with the dimension formula for the case of bosonic target existing in the literature. |
| title | Moduli of stable supermaps |
| topic | Algebraic Geometry High Energy Physics - Theory Mathematical Physics Primary: 14D23, Secondary: 14A20, 14H10, 14M30, 81T30, 83E30 |
| url | https://arxiv.org/abs/2505.22233 |