Quot scheme and deformation quantization
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913397074821120 |
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| author | Biswas, Indranil |
| author_facet | Biswas, Indranil |
| contents | Let $X$ be a compact connected Riemann surface, and let ${\mathcal Q}(r,d)$ denote the quot scheme parametrizing the torsion quotients of ${\mathcal O}^{\oplus r}_X$ of degree $d$. Given a projective structure $P$ on $X$, we show that the cotangent bundle $T^*{\mathcal U}$ of a certain nonempty Zariski open subset ${\mathcal U}\, \subset\, {\mathcal Q}(r,d)$, equipped with the natural Liouville symplectic form, admits a canonical deformation quantization. When $r\,=\,1\,=\, d$, then ${\mathcal Q}(r,d)\,=\, X$; this case was addressed earlier in \cite{BB}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12836 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quot scheme and deformation quantization Biswas, Indranil Mathematical Physics Algebraic Geometry Let $X$ be a compact connected Riemann surface, and let ${\mathcal Q}(r,d)$ denote the quot scheme parametrizing the torsion quotients of ${\mathcal O}^{\oplus r}_X$ of degree $d$. Given a projective structure $P$ on $X$, we show that the cotangent bundle $T^*{\mathcal U}$ of a certain nonempty Zariski open subset ${\mathcal U}\, \subset\, {\mathcal Q}(r,d)$, equipped with the natural Liouville symplectic form, admits a canonical deformation quantization. When $r\,=\,1\,=\, d$, then ${\mathcal Q}(r,d)\,=\, X$; this case was addressed earlier in \cite{BB}. |
| title | Quot scheme and deformation quantization |
| topic | Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2406.12836 |