Quot scheme and deformation quantization
type: Item
instance of: scholarly article
title: Quot scheme and deformation quantization
author: Indranil Biswas
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2024-10-10T00:00:00Z
review text: Given a compact connected Riemannian surface \(X\)\ and a projective structure \(P\)\ on \(X\)\ with \(\mathcal{Q}\left( r,d\right) \) denoting the quot scheme parametrization of all torsion quotients of \(\mathcal{O}_{X}^{\oplus r}\)\ of degree \(d\), this paper shows (Theorem 5.1) that \(\mathcal{U}\subset T^{\ast }\mathcal{Q}\)\ rigged with the holomorphic symplectic form \(\theta _{\mathcal{U}}\), where \(\mathcal{U}\subset T^{\ast}\mathcal{Q}\)\ is a certain Zariski subset, has a natrual deformation quantization. \textit{D. Ben-Zvi} and \textit{I. Biswas} [Lett. Math. Phys. 54, No. 1, 73--82 (2000; Zbl 0979.53094)] have already addressed the case when \(r=1=d\).
reviewed by: Hirokazu Nishimura
Mathematics Subject Classification ID: 53D55
Mathematics Subject Classification ID: 81S10
Mathematics Subject Classification ID: 14H60
Mathematics Subject Classification ID: 14D21
zbMATH DE Number: 7924882
zbMATH Keywords: deformation quantization
zbMATH Keywords: projective structures
zbMATH Keywords: quot schemes
zbMATH Keywords: Moyal-Weyl deformation quantization
MaRDI profile type: Publication
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DOI: 10.1007/S12044-024-00794-2
description: scientific article; zbMATH DE number 7924882