Quot scheme and deformation quantization

2024/06/18 by Indranil Biswas, Biswas, Indranil
Computer Science · #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2406.12836

openalex publication_date 2024/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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^{⊕ 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 ⊂ \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 \citeBB.

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