A Simple Recursion for the Mirzakhani Volume and its Super Extension
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866917863165526016 |
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| author | Du, Yukun |
| author_facet | Du, Yukun |
| contents | In this paper, we derive a simple recursion formula for the Weil-Petersson volumes of moduli spaces of hyperbolic surfaces with boundaries. This formula demonstrates the polynomiality of the volume functions. By constructing the Laplace transform for both the original and our alternative formulas, we show that they are directly equivalent. By considering the top and lowest degree terms of these formulas, we recover the DVV identity and cohomology class identities for $\mathcal{M}_{g,n}$. Similar conclusions are drawn for the super-analog of these results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_04458 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A Simple Recursion for the Mirzakhani Volume and its Super Extension Du, Yukun Algebraic Geometry Mathematical Physics 14H81, 58A50 In this paper, we derive a simple recursion formula for the Weil-Petersson volumes of moduli spaces of hyperbolic surfaces with boundaries. This formula demonstrates the polynomiality of the volume functions. By constructing the Laplace transform for both the original and our alternative formulas, we show that they are directly equivalent. By considering the top and lowest degree terms of these formulas, we recover the DVV identity and cohomology class identities for $\mathcal{M}_{g,n}$. Similar conclusions are drawn for the super-analog of these results. |
| title | A Simple Recursion for the Mirzakhani Volume and its Super Extension |
| topic | Algebraic Geometry Mathematical Physics 14H81, 58A50 |
| url | https://arxiv.org/abs/2008.04458 |