Differential operators on a Riemann surface with projective structure

Biswas, Indranil (2004) Differential operators on a Riemann surface with projective structure Journal of Geometry and Physics, 50 (1-4). pp. 393-414. ISSN 0393-0440

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S03930...

Related URL: http://dx.doi.org/10.1016/j.geomphys.2003.09.002


Let X be a Riemann surface equipped with a projective structure p and L a theta characteristic on X, or in other words, L is a holomorphic line bundle equipped with a holomorphic isomorphism with the holomorphic cotangent bundle ΩX. The complement of the zero section in the total space of the line bundle L has a natural holomorphic symplectic structure, and using p, this symplectic structure has a canonical quantization. Using this quantization, holomorphic differential operators on X are constructed. The main result is the construction of a canonical isomorphism H0(X,DiffkX(L⊗j,L⊗(i+j+2k)))≅⊕l=0kH0(X,L⊗i⊗ Ωx⊗l), i,j∈Z, n≤ 0, provided i∉[-2(k-1),0].

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Differential operator; Projective structure; Quantization
ID Code:3614
Deposited On:18 Oct 2010 10:19
Last Modified:27 Jan 2011 09:09

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