Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2411.10348 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913578869587968 |
|---|---|
| author | Hamilton, Mark Karshon, Yael Yoshida, Takahiko |
| author_facet | Hamilton, Mark Karshon, Yael Yoshida, Takahiko |
| contents | We give a simple proof that, for a pre-quantized compact symplectic manifold with a Lagrangian torus fibration, its Riemann-Roch number coincides with its number of Bohr-Sommerfeld fibres. This can be viewed as an instance of the "independence of polarization" phenomenon of geometric quantization. The base space for such a fibration acquires a so-called integral-integral affine structure. The proof uses the following simple fact, whose proof is trickier than we expected: on a compact integral-integral affine manifold, the total volume is equal to the number of integer points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10348 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integral-integral affine geometry, geometric quantization, and Riemann-Roch Hamilton, Mark Karshon, Yael Yoshida, Takahiko Symplectic Geometry 53D50, 53C15 We give a simple proof that, for a pre-quantized compact symplectic manifold with a Lagrangian torus fibration, its Riemann-Roch number coincides with its number of Bohr-Sommerfeld fibres. This can be viewed as an instance of the "independence of polarization" phenomenon of geometric quantization. The base space for such a fibration acquires a so-called integral-integral affine structure. The proof uses the following simple fact, whose proof is trickier than we expected: on a compact integral-integral affine manifold, the total volume is equal to the number of integer points. |
| title | Integral-integral affine geometry, geometric quantization, and Riemann-Roch |
| topic | Symplectic Geometry 53D50, 53C15 |
| url | https://arxiv.org/abs/2411.10348 |