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arXiv · 2406.12836

Quot scheme and deformation quantization

Indranil Biswas
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Abstract

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}.

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Indranil Biswas. 2024-06-18. Quot scheme and deformation quantization. https://arxiv.org/abs/2406.12836

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