The weighted projective superspace with weights $+1, -1$ and an analog of the Fubini--Study form
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913237069463552 |
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| author | Shemyakova, Ekaterina Voronov, Theodore |
| author_facet | Shemyakova, Ekaterina Voronov, Theodore |
| contents | As a by-product of our work on super Plücker embedding, we came to the notion of a weighted projective superspace $P_{+1,-1}(V\oplus W)$ with weights $+1,-1$. The construction is not in itself super and makes sense in ordinary (purely even) framework. Unlike the familiar weighted projective spaces with positive weights, the (super)space $P_{+1,-1}(V\oplus W)$ is a smooth (super)manifold. We describe its structure and show that it possesses an analog of the Fubini--Study form. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_11860 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The weighted projective superspace with weights $+1, -1$ and an analog of the Fubini--Study form Shemyakova, Ekaterina Voronov, Theodore Differential Geometry Mathematical Physics Algebraic Geometry As a by-product of our work on super Plücker embedding, we came to the notion of a weighted projective superspace $P_{+1,-1}(V\oplus W)$ with weights $+1,-1$. The construction is not in itself super and makes sense in ordinary (purely even) framework. Unlike the familiar weighted projective spaces with positive weights, the (super)space $P_{+1,-1}(V\oplus W)$ is a smooth (super)manifold. We describe its structure and show that it possesses an analog of the Fubini--Study form. |
| title | The weighted projective superspace with weights $+1, -1$ and an analog of the Fubini--Study form |
| topic | Differential Geometry Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2402.11860 |